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

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

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

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

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

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

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

Solving
-6 + 1w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(2 + -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 '(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 = {-3, 2}