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

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

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

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

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

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

Combine like terms: 2w + -6w = -4w
(-12 + -4w + w2) = 0

Solving
-12 + -4w + w2 = 0

Solving for variable 'w'.

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

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}