(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 = -5w
(6 + -5w + w2) = 0

Solving
6 + -5w + w2 = 0

Solving for variable 'w'.

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