2(w^2+5w-36)-168=w^2+9w

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Solution for 2(w^2+5w-36)-168=w^2+9w equation: 


Simplifying
2(w2 + 5w + -36) + -168 = w2 + 9w

Reorder the terms:
2(-36 + 5w + w2) + -168 = w2 + 9w
(-36 * 2 + 5w * 2 + w2 * 2) + -168 = w2 + 9w
(-72 + 10w + 2w2) + -168 = w2 + 9w

Reorder the terms:
-72 + -168 + 10w + 2w2 = w2 + 9w

Combine like terms: -72 + -168 = -240
-240 + 10w + 2w2 = w2 + 9w

Reorder the terms:
-240 + 10w + 2w2 = 9w + w2

Solving
-240 + 10w + 2w2 = 9w + w2

Solving for variable 'w'.

Reorder the terms:
-240 + 10w + -9w + 2w2 + -1w2 = 9w + w2 + -9w + -1w2

Combine like terms: 10w + -9w = 1w
-240 + 1w + 2w2 + -1w2 = 9w + w2 + -9w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-240 + 1w + 1w2 = 9w + w2 + -9w + -1w2

Reorder the terms:
-240 + 1w + 1w2 = 9w + -9w + w2 + -1w2

Combine like terms: 9w + -9w = 0
-240 + 1w + 1w2 = 0 + w2 + -1w2
-240 + 1w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-240 + 1w + 1w2 = 0

Factor a trinomial.
(-16 + -1w)(15 + -1w) = 0


Subproblem 1
Set the factor '(-16 + -1w)' equal to zero and attempt to solve:

Simplifying
-16 + -1w = 0

Solving
-16 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '16' to each side of the equation.
-16 + 16 + -1w = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1w = 0 + 16
-1w = 0 + 16

Combine like terms: 0 + 16 = 16
-1w = 16

Divide each side by '-1'.
w = -16

Simplifying
w = -16

Subproblem 2
Set the factor '(15 + -1w)' equal to zero and attempt to solve:

Simplifying
15 + -1w = 0

Solving
15 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-15' to each side of the equation.
15 + -15 + -1w = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1w = 0 + -15
-1w = 0 + -15

Combine like terms: 0 + -15 = -15
-1w = -15

Divide each side by '-1'.
w = 15

Simplifying
w = 15
Solution
w = {-16, 15}

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