We know that this equation can be simplified to the following format:

(X+_)(X+_) = 0

X will be cross-multiplied by X to form the  of the equation. We need to plug in number values that will result in 4x and 3 when cross-multiplied:

(X+3) = 0, X = -3

(X+1) = 0, X = -1

When looking at the equation, it is clear that both coefficients and the number value are divisible by 5:

So our first step is to divide both sides of the equation by 5:

When further simplified, we get:

When we plug in the X-Value, we can confirm whether or not this is the correct value for X:

Thus we can confirm that this is the correct value for X. 

The first step to this quadratic equation is to divide it by the least common denominator, which in this case is 2:

Next, we plug the equation into the Quadratic Formula:

 and/or 

 and/or 

We now have 2 possible values for X. The next step is to plug both values in to determine if they are correct values of X:

After confirming both values for X work when plugged into the quadratic formula, we can confirm:

 and 

Since this is a quadratic formula and X-squared has a coefficient of 1, the simplified equation will be in the following format:

Looking at the simplified equation and the quadratic equation above, we can see that the numerical values we plug in need to sum up to 6X and have a product of -16 when cross-multiplied. 

If we plug in 8 and -2, we will get the original equation when we cross-multiply:

To double check our answers, we can plug them in to make sure they make sense:

1) Quadratics must be set equal to zero in order to be solved. To do so in this equation, the "8" has to wind up on the left side and combine with any other lone integers. So, multiply out the terms in order to make it possible for the "8" to be added to the other number.

Then combine like terms.

2) Now factor.

1 + 16 = 17

4 + 4 = 8

2 + 8 = 10

3) Pull out common factors, "x" and "8," respectively.

4) Pull out "(x+2)" from both terms.

x = –8, –2

1) Combine like terms and simplify.

No further simplification is possible. The first term has a coefficient that can't be factored away. FOIL requires that all terms be multiplied by each other at some point, so the presence of the coefficient has to be reflected in every step of the factoring.

2) Practically speaking, that means we add an extra step. Multiply the coefficient of the first term by the last term before factoring.

3 * 6 = 18

Factors of 18 include:

1 + 18 = 19

2 + 9 = 11

3) Now pull out the common factor in each of the pairs, "3x" from the first two and "2" from the second two.

4) Pull out the "(x+3)" from both terms.

5) Set both parts equal to zero and solve.

3x + 2 = 0, x = –2/3

x + 3 = 0, x = –3

1) The first step would be to simplify, but since 2, 15, and 25 have no common factors greater than 1, simplification is impossible.

Now we factor. Multiply the first coefficient by the final term and list off the factors.

2 * 25 = 50

Factors of 50 include:

1 + 50 = 51

2 + 25 = 27

5 + 10 = 15

2) Split up the middle term to make factoring by grouping possible.

Note that the "2" and the "10," and the "5" and the "25," have to go together for factoring to come out with integers. Always make sure the groups actually have a common factor to pull.

3) Pull out the common factors from both groups, "2x" from the first and "5" from the second.

4) Factor out the "(x+5)" from both terms.

5) Set each parenthetical expression equal to zero and solve.

2x + 5 = 0,  x = –5/2

x + 5 = 0, x = –5

The quadratic formula is as follows:

We will start by finding the values of the coefficients of the given equation:

Quadratic equations may be written in the following format:

In our case, the values of the coefficients are:

Substitute the coefficient values into the quadratic equation:

After simplifying we are left with:

leaving us with our two solutions:

 and 

Use the quadratic equation: 

and use the general formula

to find the coefficients.

In our case,  thus, , , .

Plugging our values into the quadratic equation we are able to solve for .

Our first step is to factor the expression. We must find two numbers which have a sum of -4 and a product of -32. -32 can be factored into +/-2 and -/+16, or +/-4 and -/+8. The only combination that satisfies the product and sum is +4 and -8. 

This means we can factor our expression to . 

To find the zeroes, we simply need to find where our expression equals zero. And we can find this easily by determining where (x+4) and (x-8) each equal zero.

The zeroes of our expression, then, are at -4 and 8. 

and