(-w+6)(3w-6)=0

Solution for (-w+6)(3w-6)=0 equation:

Simplifying
(-1w + 6)(3w + -6) = 0

Reorder the terms:
(6 + -1w)(3w + -6) = 0

Reorder the terms:
(6 + -1w)(-6 + 3w) = 0

Multiply (6 + -1w) * (-6 + 3w)
(6(-6 + 3w) + -1w * (-6 + 3w)) = 0
((-6 * 6 + 3w * 6) + -1w * (-6 + 3w)) = 0
((-36 + 18w) + -1w * (-6 + 3w)) = 0
(-36 + 18w + (-6 * -1w + 3w * -1w)) = 0
(-36 + 18w + (6w + -3w2)) = 0

Combine like terms: 18w + 6w = 24w
(-36 + 24w + -3w2) = 0

Solving
-36 + 24w + -3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 8w + -1w2) = 0

Factor a trinomial.
3((-6 + w)(2 + -1w)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
w = {6, 2}