w(4w-9)=90

Solution for w(4w-9)=90 equation:

Simplifying
w(4w + -9) = 90

Reorder the terms:
w(-9 + 4w) = 90
(-9 * w + 4w * w) = 90
(-9w + 4w2) = 90

Solving
-9w + 4w2 = 90

Solving for variable 'w'.

Reorder the terms:
-90 + -9w + 4w2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -9w + 4w2 = 0

Factor a trinomial.
(-15 + -4w)(6 + -1w) = 0

Subproblem 1
Set the factor '(-15 + -4w)' equal to zero and attempt to solve:

Simplifying
-15 + -4w = 0

Solving
-15 + -4w = 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 + -4w = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4w = 0 + 15
-4w = 0 + 15

Combine like terms: 0 + 15 = 15
-4w = 15

Divide each side by '-4'.
w = -3.75

Simplifying
w = -3.75
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 = {-3.75, 6}