32=-4w+w^2

Solution for 32=-4w+w^2 equation:

Simplifying
32 = -4w + w2

Solving
32 = -4w + w2

Solving for variable 'w'.

Reorder the terms:
32 + 4w + -1w2 = -4w + 4w + w2 + -1w2

Combine like terms: -4w + 4w = 0
32 + 4w + -1w2 = 0 + w2 + -1w2
32 + 4w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
32 + 4w + -1w2 = 0

Factor a trinomial.
(8 + -1w)(4 + w) = 0

Subproblem 1
Set the factor '(8 + -1w)' equal to zero and attempt to solve:

Simplifying
8 + -1w = 0

Solving
8 + -1w = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1w = 0 + -8
-1w = 0 + -8

Combine like terms: 0 + -8 = -8
-1w = -8

Divide each side by '-1'.
w = 8

Simplifying
w = 8
Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 0

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

Add '-4' to each side of the equation.
4 + -4 + w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + w = 0 + -4
w = 0 + -4

Combine like terms: 0 + -4 = -4
w = -4

Simplifying
w = -4
Solution
w = {8, -4}