96=w(4+w)

Solution for 96=w(4+w) equation:

Simplifying
96 = w(4 + w)
96 = (4 * w + w * w)
96 = (4w + w2)

Solving
96 = 4w + w2

Solving for variable 'w'.

Reorder the terms:
96 + -4w + -1w2 = 4w + -4w + w2 + -1w2

Combine like terms: 4w + -4w = 0
96 + -4w + -1w2 = 0 + w2 + -1w2
96 + -4w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
96 + -4w + -1w2 = 0

Factor a trinomial.
(8 + -1w)(12 + 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 '(12 + w)' equal to zero and attempt to solve:

Simplifying
12 + w = 0

Solving
12 + w = 0

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

Add '-12' to each side of the equation.
12 + -12 + w = 0 + -12

Combine like terms: 12 + -12 = 0
0 + w = 0 + -12
w = 0 + -12

Combine like terms: 0 + -12 = -12
w = -12

Simplifying
w = -12
Solution
w = {8, -12}