88=(3+w)*w

Solution for 88=(3+w)*w equation:

Simplifying
88 = (3 + w) * w

Reorder the terms for easier multiplication:
88 = w(3 + w)
88 = (3 * w + w * w)
88 = (3w + w2)

Solving
88 = 3w + w2

Solving for variable 'w'.

Reorder the terms:
88 + -3w + -1w2 = 3w + -3w + w2 + -1w2

Combine like terms: 3w + -3w = 0
88 + -3w + -1w2 = 0 + w2 + -1w2
88 + -3w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
88 + -3w + -1w2 = 0

Factor a trinomial.
(8 + -1w)(11 + 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 '(11 + w)' equal to zero and attempt to solve:

Simplifying
11 + w = 0

Solving
11 + w = 0

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

Add '-11' to each side of the equation.
11 + -11 + w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + w = 0 + -11
w = 0 + -11

Combine like terms: 0 + -11 = -11
w = -11

Simplifying
w = -11
Solution
w = {8, -11}