w(9+w)=(18+2w)(w-4)-84

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Solution for w(9+w)=(18+2w)(w-4)-84 equation: 


Simplifying
w(9 + w) = (18 + 2w)(w + -4) + -84
(9 * w + w * w) = (18 + 2w)(w + -4) + -84
(9w + w2) = (18 + 2w)(w + -4) + -84

Reorder the terms:
9w + w2 = (18 + 2w)(-4 + w) + -84

Multiply (18 + 2w) * (-4 + w)
9w + w2 = (18(-4 + w) + 2w * (-4 + w)) + -84
9w + w2 = ((-4 * 18 + w * 18) + 2w * (-4 + w)) + -84
9w + w2 = ((-72 + 18w) + 2w * (-4 + w)) + -84
9w + w2 = (-72 + 18w + (-4 * 2w + w * 2w)) + -84
9w + w2 = (-72 + 18w + (-8w + 2w2)) + -84

Combine like terms: 18w + -8w = 10w
9w + w2 = (-72 + 10w + 2w2) + -84

Reorder the terms:
9w + w2 = -72 + -84 + 10w + 2w2

Combine like terms: -72 + -84 = -156
9w + w2 = -156 + 10w + 2w2

Solving
9w + w2 = -156 + 10w + 2w2

Solving for variable 'w'.

Reorder the terms:
156 + 9w + -10w + w2 + -2w2 = -156 + 10w + 2w2 + 156 + -10w + -2w2

Combine like terms: 9w + -10w = -1w
156 + -1w + w2 + -2w2 = -156 + 10w + 2w2 + 156 + -10w + -2w2

Combine like terms: w2 + -2w2 = -1w2
156 + -1w + -1w2 = -156 + 10w + 2w2 + 156 + -10w + -2w2

Reorder the terms:
156 + -1w + -1w2 = -156 + 156 + 10w + -10w + 2w2 + -2w2

Combine like terms: -156 + 156 = 0
156 + -1w + -1w2 = 0 + 10w + -10w + 2w2 + -2w2
156 + -1w + -1w2 = 10w + -10w + 2w2 + -2w2

Combine like terms: 10w + -10w = 0
156 + -1w + -1w2 = 0 + 2w2 + -2w2
156 + -1w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
156 + -1w + -1w2 = 0

Factor a trinomial.
(12 + -1w)(13 + w) = 0


Subproblem 1
Set the factor '(12 + -1w)' equal to zero and attempt to solve:

Simplifying
12 + -1w = 0

Solving
12 + -1w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1w = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1w = 0 + -12
-1w = 0 + -12

Combine like terms: 0 + -12 = -12
-1w = -12

Divide each side by '-1'.
w = 12

Simplifying
w = 12

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

Simplifying
13 + w = 0

Solving
13 + w = 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 + w = 0 + -13

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

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

Simplifying
w = -13
Solution
w = {12, -13}

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