(w-5)(w-9)=0

Solution for (w-5)(w-9)=0 equation:

Simplifying
(w + -5)(w + -9) = 0

Reorder the terms:
(-5 + w)(w + -9) = 0

Reorder the terms:
(-5 + w)(-9 + w) = 0

Multiply (-5 + w) * (-9 + w)
(-5(-9 + w) + w(-9 + w)) = 0
((-9 * -5 + w * -5) + w(-9 + w)) = 0
((45 + -5w) + w(-9 + w)) = 0
(45 + -5w + (-9 * w + w * w)) = 0
(45 + -5w + (-9w + w2)) = 0

Combine like terms: -5w + -9w = -14w
(45 + -14w + w2) = 0

Solving
45 + -14w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + -1w)(9 + -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 '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {5, 9}