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

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

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

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

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

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

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

Solving
-18 + -3w + w2 = 0

Solving for variable 'w'.

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

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 + -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 = {-3, 6}