w^2-18w+32=0

Solution for w^2-18w+32=0 equation:

Simplifying
w2 + -18w + 32 = 0

Reorder the terms:
32 + -18w + w2 = 0

Solving
32 + -18w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(2 + -1w)(16 + -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 '(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 = {2, 16}