90=w(2w+3)

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

Simplifying
90 = w(2w + 3)

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

Solving
90 = 3w + 2w2

Solving for variable 'w'.

Reorder the terms:
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.
(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}