w^2=32-4w

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

Simplifying
w2 = 32 + -4w

Solving
w2 = 32 + -4w

Solving for variable 'w'.

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

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

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

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

Factor a trinomial.
(-8 + -1w)(4 + -1w) = 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 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 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 + -1w = 0 + -4

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

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

Divide each side by '-1'.
w = 4

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