2(w+9)(w-4)=w^2+9w+138

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Solution for 2(w+9)(w-4)=w^2+9w+138 equation:


Simplifying
2(w + 9)(w + -4) = w2 + 9w + 138

Reorder the terms:
2(9 + w)(w + -4) = w2 + 9w + 138

Reorder the terms:
2(9 + w)(-4 + w) = w2 + 9w + 138

Multiply (9 + w) * (-4 + w)
2(9(-4 + w) + w(-4 + w)) = w2 + 9w + 138
2((-4 * 9 + w * 9) + w(-4 + w)) = w2 + 9w + 138
2((-36 + 9w) + w(-4 + w)) = w2 + 9w + 138
2(-36 + 9w + (-4 * w + w * w)) = w2 + 9w + 138
2(-36 + 9w + (-4w + w2)) = w2 + 9w + 138

Combine like terms: 9w + -4w = 5w
2(-36 + 5w + w2) = w2 + 9w + 138
(-36 * 2 + 5w * 2 + w2 * 2) = w2 + 9w + 138
(-72 + 10w + 2w2) = w2 + 9w + 138

Reorder the terms:
-72 + 10w + 2w2 = 138 + 9w + w2

Solving
-72 + 10w + 2w2 = 138 + 9w + w2

Solving for variable 'w'.

Reorder the terms:
-72 + -138 + 10w + -9w + 2w2 + -1w2 = 138 + 9w + w2 + -138 + -9w + -1w2

Combine like terms: -72 + -138 = -210
-210 + 10w + -9w + 2w2 + -1w2 = 138 + 9w + w2 + -138 + -9w + -1w2

Combine like terms: 10w + -9w = 1w
-210 + 1w + 2w2 + -1w2 = 138 + 9w + w2 + -138 + -9w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-210 + 1w + 1w2 = 138 + 9w + w2 + -138 + -9w + -1w2

Reorder the terms:
-210 + 1w + 1w2 = 138 + -138 + 9w + -9w + w2 + -1w2

Combine like terms: 138 + -138 = 0
-210 + 1w + 1w2 = 0 + 9w + -9w + w2 + -1w2
-210 + 1w + 1w2 = 9w + -9w + w2 + -1w2

Combine like terms: 9w + -9w = 0
-210 + 1w + 1w2 = 0 + w2 + -1w2
-210 + 1w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-210 + 1w + 1w2 = 0

Factor a trinomial.
(-15 + -1w)(14 + -1w) = 0


Subproblem 1
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

Subproblem 2
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
Solution
w = {-15, 14}

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