90=(2w)(2w)+2w

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

Simplifying
90 = (2w)(2w) + 2w

Remove parenthesis around (2w)
90 = 2w(2w) + 2w

Remove parenthesis around (2w)
90 = 2w * 2w + 2w

Reorder the terms for easier multiplication:
90 = 2 * 2w * w + 2w

Multiply 2 * 2
90 = 4w * w + 2w

Multiply w * w
90 = 4w2 + 2w

Reorder the terms:
90 = 2w + 4w2

Solving
90 = 2w + 4w2

Solving for variable 'w'.

Reorder the terms:
90 + -2w + -4w2 = 2w + -2w + 4w2 + -4w2

Combine like terms: 2w + -2w = 0
90 + -2w + -4w2 = 0 + 4w2 + -4w2
90 + -2w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
90 + -2w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + -1w + -2w2) = 0

Factor a trinomial.
2((9 + -2w)(5 + w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + -2w)' equal to zero and attempt to solve:

Simplifying
9 + -2w = 0

Solving
9 + -2w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2w = 0 + -9
-2w = 0 + -9

Combine like terms: 0 + -9 = -9
-2w = -9

Divide each side by '-2'.
w = 4.5

Simplifying
w = 4.5
Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Solution
w = {4.5, -5}