Add 8 to both sides to set the equation equal to 0:

To factor, find two integers that multiply to 24 and add to 10.  4 and 6 satisfy both conditions. Thus, we can rewrite the quadratic of three terms as a quadratic of four terms, using the the two integers we just found to split the middle coefficient:

Then factor by grouping:

Set each factor equal to 0 and solve:

and

First, find the factors of 90 and 315.  The greatest common factor is the largest factor shared by both of the numbers: 45.

Then, find the least common multiple of 5 and 15.  This will be the smallest number that can be divided by both 5 and 15: 15.

Finally, the greatest common factor (45) divided by the least common multiple (15) = 45 / 15 = 3.

The given expression is a special binomial, known as the "difference of squares". A difference of squares binomial has the given factorization: . Thus, we can rewrite  as  and it follows that 

The product of is .

For the equation , 

must equal and  must equal .

Thus  and must be and , making the answer  .

This is a quadratic equation. We can solve  for either by factoring or using the quadratic formula. Since this equation is factorable, I will present the factoring method here.

The factored form of our equation should be in the format .

To yield the first value in our original equation (),  and .

To yield the final term in our original equation (), we can set  and .

Now that the equation has been factored, we can evaluate . We set each factored term equal to zero and solve.

First factor the numerator. We need two numbers with a sum of 3 and a product of 2. The numbers 1 and 2 satisfy these conditions:

Now, look to see if there are any common factors that will cancel:

The  in the numerator and denominator cancel, leaving .

The general form for a factored expression of order 2 is 

, which, when FOILED, gives .

Comparing this generic expression to the one given in the probem, we can see that the  term should equal , and the  term should equal 2.

The values of  and  that satisfy the two equations are  and ,

so your factored expression is 

The first step in solving the equation is to add  to both sides so that we can set the new equation equal to  so that we can factor it.

We now need to factor it. We need to find two numbers,  and , such that  and .

Those two numbers are 

Our new factored expression becomes

Now we can easily identify that the values that satisfy this equation are .

In order to set this up for completing the square, we need to move the 135 to the other side:

Now the equation is in the form:

To complete the square we need to add to both sides the folowing value:

So we need to add 9 to both sides of the equation:

Now we can factor the left side and simplify the left side:

Now we need to take the square root of both sides:

**NOTE: Don't foget to add the plus or minus symbol. We add this becase there are two values we can square to get 144:

and

**End note

Now we can split into two equations and solve for x:

and

So our solution is:

There is a common variable  in each term.  Pull this out as a common factor.

Factor  .

The common factors that will achieve the middle term and will have a product of 36 is four and nine.  Write the binomials.

The cubics here cannot be simplified any further.

The answer is: