(4+2w)(w)=160

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Solution for (4+2w)(w)=160 equation: 


Simplifying
(4 + 2w)(w) = 160

Reorder the terms for easier multiplication:
w(4 + 2w) = 160
(4 * w + 2w * w) = 160
(4w + 2w2) = 160

Solving
4w + 2w2 = 160

Solving for variable 'w'.

Reorder the terms:
-160 + 4w + 2w2 = 160 + -160

Combine like terms: 160 + -160 = 0
-160 + 4w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-80 + 2w + w2) = 0

Factor a trinomial.
2((-10 + -1w)(8 + -1w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve:

Simplifying
-10 + -1w = 0

Solving
-10 + -1w = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1w = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1w = 0 + 10
-1w = 0 + 10

Combine like terms: 0 + 10 = 10
-1w = 10

Divide each side by '-1'.
w = -10

Simplifying
w = -10

Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve:

Simplifying
8 + -1w = 0

Solving
8 + -1w = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1w = 0 + -8
-1w = 0 + -8

Combine like terms: 0 + -8 = -8
-1w = -8

Divide each side by '-1'.
w = 8

Simplifying
w = 8
Solution
w = {-10, 8}

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