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

1) Begin the problem by factoring the final term. Include the negative when factoring.

–2 + 2 = 0

–4 + 1 = –3

–1 + 4 = 3

All options are exhausted, therefore the problem cannot be solved by factoring, which means that the roots either do not exist or are not rational numbers. We must use the quadratic formula.

Put the quadratic in standard form:

Factor:

An easy way to factor (and do so with less trial and error) is to think of what two numbers could multiply to equal "c", but add to equal "b". These letters come from the designations in the standard form of a quadratic equation: . As you can see the product of -6 and 2 is -12 and they both add to 4.

Use the quadratic formula to solve the equation.

Plug in these values and solve.