0=w(2w-3)-90

Solution for 0=w(2w-3)-90 equation:

Simplifying
0 = w(2w + -3) + -90

Reorder the terms:
0 = w(-3 + 2w) + -90
0 = (-3 * w + 2w * w) + -90
0 = (-3w + 2w2) + -90

Reorder the terms:
0 = -90 + -3w + 2w2

Solving
0 = -90 + -3w + 2w2

Solving for variable 'w'.

Combine like terms: 0 + 90 = 90
90 + 3w + -2w2 = -90 + -3w + 2w2 + 90 + 3w + -2w2

Reorder the terms:
90 + 3w + -2w2 = -90 + 90 + -3w + 3w + 2w2 + -2w2

Combine like terms: -90 + 90 = 0
90 + 3w + -2w2 = 0 + -3w + 3w + 2w2 + -2w2
90 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2

Combine like terms: -3w + 3w = 0
90 + 3w + -2w2 = 0 + 2w2 + -2w2
90 + 3w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
90 + 3w + -2w2 = 0

Factor a trinomial.
(15 + -2w)(6 + w) = 0

Subproblem 1
Set the factor '(15 + -2w)' equal to zero and attempt to solve:

Simplifying
15 + -2w = 0

Solving
15 + -2w = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2w = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2w = 0 + -15
-2w = 0 + -15

Combine like terms: 0 + -15 = -15
-2w = -15

Divide each side by '-2'.
w = 7.5

Simplifying
w = 7.5
Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Solution
w = {7.5, -6}