234=(2w+8)w

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Solution for 234=(2w+8)w equation: 


Simplifying
234 = (2w + 8) * w

Reorder the terms:
234 = (8 + 2w) * w

Reorder the terms for easier multiplication:
234 = w(8 + 2w)
234 = (8 * w + 2w * w)
234 = (8w + 2w2)

Solving
234 = 8w + 2w2

Solving for variable 'w'.

Reorder the terms:
234 + -8w + -2w2 = 8w + -8w + 2w2 + -2w2

Combine like terms: 8w + -8w = 0
234 + -8w + -2w2 = 0 + 2w2 + -2w2
234 + -8w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
234 + -8w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(117 + -4w + -1w2) = 0

Factor a trinomial.
2((9 + -1w)(13 + w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

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

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

Divide each side by '-1'.
w = 9

Simplifying
w = 9

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 = {9, -13}

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