18w+w^2-88=0

Solution for 18w+w^2-88=0 equation:

Simplifying
18w + w2 + -88 = 0

Reorder the terms:
-88 + 18w + w2 = 0

Solving
-88 + 18w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-22 + -1w)(4 + -1w) = 0

Subproblem 1
Set the factor '(-22 + -1w)' equal to zero and attempt to solve:

Simplifying
-22 + -1w = 0

Solving
-22 + -1w = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1w = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1w = 0 + 22
-1w = 0 + 22

Combine like terms: 0 + 22 = 22
-1w = 22

Divide each side by '-1'.
w = -22

Simplifying
w = -22
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 = {-22, 4}