(42-2w)(36-2w)=520

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Solution for (42-2w)(36-2w)=520 equation:


Simplifying
(42 + -2w)(36 + -2w) = 520

Multiply (42 + -2w) * (36 + -2w)
(42(36 + -2w) + -2w * (36 + -2w)) = 520
((36 * 42 + -2w * 42) + -2w * (36 + -2w)) = 520
((1512 + -84w) + -2w * (36 + -2w)) = 520
(1512 + -84w + (36 * -2w + -2w * -2w)) = 520
(1512 + -84w + (-72w + 4w2)) = 520

Combine like terms: -84w + -72w = -156w
(1512 + -156w + 4w2) = 520

Solving
1512 + -156w + 4w2 = 520

Solving for variable 'w'.

Reorder the terms:
1512 + -520 + -156w + 4w2 = 520 + -520

Combine like terms: 1512 + -520 = 992
992 + -156w + 4w2 = 520 + -520

Combine like terms: 520 + -520 = 0
992 + -156w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(248 + -39w + w2) = 0

Factor a trinomial.
4((8 + -1w)(31 + -1w)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(31 + -1w)' equal to zero and attempt to solve:

Simplifying
31 + -1w = 0

Solving
31 + -1w = 0

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

Add '-31' to each side of the equation.
31 + -31 + -1w = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -1w = 0 + -31
-1w = 0 + -31

Combine like terms: 0 + -31 = -31
-1w = -31

Divide each side by '-1'.
w = 31

Simplifying
w = 31
Solution
w = {8, 31}

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