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

Solution for (w-5)(w-6)=0 equation:

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

Reorder the terms:
(-5 + w)(w + -6) = 0

Reorder the terms:
(-5 + w)(-6 + w) = 0

Multiply (-5 + w) * (-6 + w)
(-5(-6 + w) + w(-6 + w)) = 0
((-6 * -5 + w * -5) + w(-6 + w)) = 0
((30 + -5w) + w(-6 + w)) = 0
(30 + -5w + (-6 * w + w * w)) = 0
(30 + -5w + (-6w + w2)) = 0

Combine like terms: -5w + -6w = -11w
(30 + -11w + w2) = 0

Solving
30 + -11w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + -1w)(6 + -1w) = 0

Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
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 = {5, 6}