w(2w+12)=432

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Solution for w(2w+12)=432 equation: 


Simplifying
w(2w + 12) = 432

Reorder the terms:
w(12 + 2w) = 432
(12 * w + 2w * w) = 432
(12w + 2w2) = 432

Solving
12w + 2w2 = 432

Solving for variable 'w'.

Reorder the terms:
-432 + 12w + 2w2 = 432 + -432

Combine like terms: 432 + -432 = 0
-432 + 12w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-216 + 6w + w2) = 0

Factor a trinomial.
2((-18 + -1w)(12 + -1w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-18 + -1w)' equal to zero and attempt to solve:

Simplifying
-18 + -1w = 0

Solving
-18 + -1w = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1w = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1w = 0 + 18
-1w = 0 + 18

Combine like terms: 0 + 18 = 18
-1w = 18

Divide each side by '-1'.
w = -18

Simplifying
w = -18

Subproblem 2
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
Solution
w = {-18, 12}

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