2(2w-4)(w-4)=32

Solution for 2(2w-4)(w-4)=32 equation:

Simplifying
2(2w + -4)(w + -4) = 32

Reorder the terms:
2(-4 + 2w)(w + -4) = 32

Reorder the terms:
2(-4 + 2w)(-4 + w) = 32

Multiply (-4 + 2w) * (-4 + w)
2(-4(-4 + w) + 2w * (-4 + w)) = 32
2((-4 * -4 + w * -4) + 2w * (-4 + w)) = 32
2((16 + -4w) + 2w * (-4 + w)) = 32
2(16 + -4w + (-4 * 2w + w * 2w)) = 32
2(16 + -4w + (-8w + 2w2)) = 32

Combine like terms: -4w + -8w = -12w
2(16 + -12w + 2w2) = 32
(16 * 2 + -12w * 2 + 2w2 * 2) = 32
(32 + -24w + 4w2) = 32

Add '-32' to each side of the equation.
32 + -24w + -32 + 4w2 = 32 + -32

Reorder the terms:
32 + -32 + -24w + 4w2 = 32 + -32

Combine like terms: 32 + -32 = 0
0 + -24w + 4w2 = 32 + -32
-24w + 4w2 = 32 + -32

Combine like terms: 32 + -32 = 0
-24w + 4w2 = 0

Solving
-24w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4w'.
4w(-6 + w) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
Set the factor '(-6 + w)' equal to zero and attempt to solve:

Simplifying
-6 + w = 0

Solving
-6 + w = 0

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

Add '6' to each side of the equation.
-6 + 6 + w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + w = 0 + 6
w = 0 + 6

Combine like terms: 0 + 6 = 6
w = 6

Simplifying
w = 6
Solution
w = {0, 6}