(32+2w)(16+2w)=1092

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Solution for (32+2w)(16+2w)=1092 equation:


Simplifying
(32 + 2w)(16 + 2w) = 1092

Multiply (32 + 2w) * (16 + 2w)
(32(16 + 2w) + 2w * (16 + 2w)) = 1092
((16 * 32 + 2w * 32) + 2w * (16 + 2w)) = 1092
((512 + 64w) + 2w * (16 + 2w)) = 1092
(512 + 64w + (16 * 2w + 2w * 2w)) = 1092
(512 + 64w + (32w + 4w2)) = 1092

Combine like terms: 64w + 32w = 96w
(512 + 96w + 4w2) = 1092

Solving
512 + 96w + 4w2 = 1092

Solving for variable 'w'.

Reorder the terms:
512 + -1092 + 96w + 4w2 = 1092 + -1092

Combine like terms: 512 + -1092 = -580
-580 + 96w + 4w2 = 1092 + -1092

Combine like terms: 1092 + -1092 = 0
-580 + 96w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-145 + 24w + w2) = 0

Factor a trinomial.
4((-29 + -1w)(5 + -1w)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-29 + -1w)' equal to zero and attempt to solve:

Simplifying
-29 + -1w = 0

Solving
-29 + -1w = 0

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

Add '29' to each side of the equation.
-29 + 29 + -1w = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -1w = 0 + 29
-1w = 0 + 29

Combine like terms: 0 + 29 = 29
-1w = 29

Divide each side by '-1'.
w = -29

Simplifying
w = -29

Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-29, 5}

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