2(w^2+5w-36)-110=w^2+9w

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Solution for 2(w^2+5w-36)-110=w^2+9w equation: 


Simplifying
2(w2 + 5w + -36) + -110 = w2 + 9w

Reorder the terms:
2(-36 + 5w + w2) + -110 = w2 + 9w
(-36 * 2 + 5w * 2 + w2 * 2) + -110 = w2 + 9w
(-72 + 10w + 2w2) + -110 = w2 + 9w

Reorder the terms:
-72 + -110 + 10w + 2w2 = w2 + 9w

Combine like terms: -72 + -110 = -182
-182 + 10w + 2w2 = w2 + 9w

Reorder the terms:
-182 + 10w + 2w2 = 9w + w2

Solving
-182 + 10w + 2w2 = 9w + w2

Solving for variable 'w'.

Reorder the terms:
-182 + 10w + -9w + 2w2 + -1w2 = 9w + w2 + -9w + -1w2

Combine like terms: 10w + -9w = 1w
-182 + 1w + 2w2 + -1w2 = 9w + w2 + -9w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-182 + 1w + 1w2 = 9w + w2 + -9w + -1w2

Reorder the terms:
-182 + 1w + 1w2 = 9w + -9w + w2 + -1w2

Combine like terms: 9w + -9w = 0
-182 + 1w + 1w2 = 0 + w2 + -1w2
-182 + 1w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-182 + 1w + 1w2 = 0

Factor a trinomial.
(-14 + -1w)(13 + -1w) = 0


Subproblem 1
Set the factor '(-14 + -1w)' equal to zero and attempt to solve:

Simplifying
-14 + -1w = 0

Solving
-14 + -1w = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1w = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1w = 0 + 14
-1w = 0 + 14

Combine like terms: 0 + 14 = 14
-1w = 14

Divide each side by '-1'.
w = -14

Simplifying
w = -14

Subproblem 2
Set the factor '(13 + -1w)' equal to zero and attempt to solve:

Simplifying
13 + -1w = 0

Solving
13 + -1w = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1w = 0 + -13
-1w = 0 + -13

Combine like terms: 0 + -13 = -13
-1w = -13

Divide each side by '-1'.
w = 13

Simplifying
w = 13
Solution
w = {-14, 13}

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