-4(w-6)(-w+2)=0

Solution for -4(w-6)(-w+2)=0 equation:

Simplifying
-4(w + -6)(-1w + 2) = 0

Reorder the terms:
-4(-6 + w)(-1w + 2) = 0

Reorder the terms:
-4(-6 + w)(2 + -1w) = 0

Multiply (-6 + w) * (2 + -1w)
-4(-6(2 + -1w) + w(2 + -1w)) = 0
-4((2 * -6 + -1w * -6) + w(2 + -1w)) = 0
-4((-12 + 6w) + w(2 + -1w)) = 0
-4(-12 + 6w + (2 * w + -1w * w)) = 0
-4(-12 + 6w + (2w + -1w2)) = 0

Combine like terms: 6w + 2w = 8w
-4(-12 + 8w + -1w2) = 0
(-12 * -4 + 8w * -4 + -1w2 * -4) = 0
(48 + -32w + 4w2) = 0

Solving
48 + -32w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + -8w + w2) = 0

Factor a trinomial.
4((2 + -1w)(6 + -1w)) = 0

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 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 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {2, 6}