w(2w-3)=90

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

Simplifying
w(2w + -3) = 90

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

Solving
-3w + 2w2 = 90

Solving for variable 'w'.

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

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

Factor a trinomial.
(-6 + -1w)(15 + -2w) = 0

Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve:

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 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 + -1w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1w = 0 + 6
-1w = 0 + 6

Combine like terms: 0 + 6 = 6
-1w = 6

Divide each side by '-1'.
w = -6

Simplifying
w = -6
Subproblem 2
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
Solution
w = {-6, 7.5}