(12-2w)(6-2w)=40

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Solution for (12-2w)(6-2w)=40 equation: 


Simplifying
(12 + -2w)(6 + -2w) = 40

Multiply (12 + -2w) * (6 + -2w)
(12(6 + -2w) + -2w * (6 + -2w)) = 40
((6 * 12 + -2w * 12) + -2w * (6 + -2w)) = 40
((72 + -24w) + -2w * (6 + -2w)) = 40
(72 + -24w + (6 * -2w + -2w * -2w)) = 40
(72 + -24w + (-12w + 4w2)) = 40

Combine like terms: -24w + -12w = -36w
(72 + -36w + 4w2) = 40

Solving
72 + -36w + 4w2 = 40

Solving for variable 'w'.

Reorder the terms:
72 + -40 + -36w + 4w2 = 40 + -40

Combine like terms: 72 + -40 = 32
32 + -36w + 4w2 = 40 + -40

Combine like terms: 40 + -40 = 0
32 + -36w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -9w + w2) = 0

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

Ignore the factor 4.

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1

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 = {1, 8}

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