w^2-22w+96=0

Solution for w^2-22w+96=0 equation:

Simplifying
w2 + -22w + 96 = 0

Reorder the terms:
96 + -22w + w2 = 0

Solving
96 + -22w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + -1w)(16 + -1w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(16 + -1w)' equal to zero and attempt to solve:

Simplifying
16 + -1w = 0

Solving
16 + -1w = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1w = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1w = 0 + -16
-1w = 0 + -16

Combine like terms: 0 + -16 = -16
-1w = -16

Divide each side by '-1'.
w = 16

Simplifying
w = 16
Solution
w = {6, 16}