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

Solution for 2(w-3)(-w-6)=0 equation:

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

Reorder the terms:
2(-3 + w)(-1w + -6) = 0

Reorder the terms:
2(-3 + w)(-6 + -1w) = 0

Multiply (-3 + w) * (-6 + -1w)
2(-3(-6 + -1w) + w(-6 + -1w)) = 0
2((-6 * -3 + -1w * -3) + w(-6 + -1w)) = 0
2((18 + 3w) + w(-6 + -1w)) = 0
2(18 + 3w + (-6 * w + -1w * w)) = 0
2(18 + 3w + (-6w + -1w2)) = 0

Combine like terms: 3w + -6w = -3w
2(18 + -3w + -1w2) = 0
(18 * 2 + -3w * 2 + -1w2 * 2) = 0
(36 + -6w + -2w2) = 0

Solving
36 + -6w + -2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -3w + -1w2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
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 = {3, -6}