32=(4+w)w

Solution for 32=(4+w)w equation:

Simplifying
32 = (4 + w) * w

Reorder the terms for easier multiplication:
32 = w(4 + w)
32 = (4 * w + w * w)
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.
(4 + -1w)(8 + w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 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 + w = 0 + -8

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

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

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