(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.
(-15 + -2w)(6 + -1w) = 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 + -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
Solution
w = {-7.5, 6}