(32+2w)(16+2w)=960

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Solution for (32+2w)(16+2w)=960 equation:


Simplifying
(32 + 2w)(16 + 2w) = 960

Multiply (32 + 2w) * (16 + 2w)
(32(16 + 2w) + 2w * (16 + 2w)) = 960
((16 * 32 + 2w * 32) + 2w * (16 + 2w)) = 960
((512 + 64w) + 2w * (16 + 2w)) = 960
(512 + 64w + (16 * 2w + 2w * 2w)) = 960
(512 + 64w + (32w + 4w2)) = 960

Combine like terms: 64w + 32w = 96w
(512 + 96w + 4w2) = 960

Solving
512 + 96w + 4w2 = 960

Solving for variable 'w'.

Reorder the terms:
512 + -960 + 96w + 4w2 = 960 + -960

Combine like terms: 512 + -960 = -448
-448 + 96w + 4w2 = 960 + -960

Combine like terms: 960 + -960 = 0
-448 + 96w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-112 + 24w + w2) = 0

Factor a trinomial.
4((-28 + -1w)(4 + -1w)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-28 + -1w)' equal to zero and attempt to solve:

Simplifying
-28 + -1w = 0

Solving
-28 + -1w = 0

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

Add '28' to each side of the equation.
-28 + 28 + -1w = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -1w = 0 + 28
-1w = 0 + 28

Combine like terms: 0 + 28 = 28
-1w = 28

Divide each side by '-1'.
w = -28

Simplifying
w = -28

Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-28, 4}

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