90=2(6+w)2w

Solution for 90=2(6+w)2w equation:

Simplifying
90 = 2(6 + w) * 2w

Reorder the terms for easier multiplication:
90 = 2 * 2w(6 + w)

Multiply 2 * 2
90 = 4w(6 + w)
90 = (6 * 4w + w * 4w)
90 = (24w + 4w2)

Solving
90 = 24w + 4w2

Solving for variable 'w'.

Reorder the terms:
90 + -24w + -4w2 = 24w + -24w + 4w2 + -4w2

Combine like terms: 24w + -24w = 0
90 + -24w + -4w2 = 0 + 4w2 + -4w2
90 + -24w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
90 + -24w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + -12w + -2w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(45 + -12w + -2w2)' equal to zero and attempt to solve:

Simplifying
45 + -12w + -2w2 = 0

Solving
45 + -12w + -2w2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-22.5 + 6w + w2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + 6w + 22.5 + w2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + 6w + w2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + 6w + w2 = 0 + 22.5
6w + w2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
6w + w2 = 22.5

The w term is 6w.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6w + 9 + w2 = 22.5 + 9

Reorder the terms:
9 + 6w + w2 = 22.5 + 9

Combine like terms: 22.5 + 9 = 31.5
9 + 6w + w2 = 31.5

Factor a perfect square on the left side:
(w + 3)(w + 3) = 31.5

Calculate the square root of the right side: 5.61248608

Break this problem into two subproblems by setting 
(w + 3) equal to 5.61248608 and -5.61248608.

Subproblem 1
w + 3 = 5.61248608

Simplifying
w + 3 = 5.61248608

Reorder the terms:
3 + w = 5.61248608

Solving
3 + w = 5.61248608

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = 5.61248608 + -3

Combine like terms: 3 + -3 = 0
0 + w = 5.61248608 + -3
w = 5.61248608 + -3

Combine like terms: 5.61248608 + -3 = 2.61248608
w = 2.61248608

Simplifying
w = 2.61248608

Subproblem 2
w + 3 = -5.61248608

Simplifying
w + 3 = -5.61248608

Reorder the terms:
3 + w = -5.61248608

Solving
3 + w = -5.61248608

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = -5.61248608 + -3

Combine like terms: 3 + -3 = 0
0 + w = -5.61248608 + -3
w = -5.61248608 + -3

Combine like terms: -5.61248608 + -3 = -8.61248608
w = -8.61248608

Simplifying
w = -8.61248608

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.61248608, -8.61248608}
Solution
w = {2.61248608, -8.61248608}