92=2w(2w+18)+2w

Solution for 92=2w(2w+18)+2w equation:

Simplifying
92 = 2w(2w + 18) + 2w

Reorder the terms:
92 = 2w(18 + 2w) + 2w
92 = (18 * 2w + 2w * 2w) + 2w
92 = (36w + 4w2) + 2w

Reorder the terms:
92 = 36w + 2w + 4w2

Combine like terms: 36w + 2w = 38w
92 = 38w + 4w2

Solving
92 = 38w + 4w2

Solving for variable 'w'.

Reorder the terms:
92 + -38w + -4w2 = 38w + -38w + 4w2 + -4w2

Combine like terms: 38w + -38w = 0
92 + -38w + -4w2 = 0 + 4w2 + -4w2
92 + -38w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
92 + -38w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(46 + -19w + -2w2) = 0

Factor a trinomial.
2((2 + -1w)(23 + 2w)) = 0

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Subproblem 2
Set the factor '(23 + 2w)' equal to zero and attempt to solve:

Simplifying
23 + 2w = 0

Solving
23 + 2w = 0

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

Add '-23' to each side of the equation.
23 + -23 + 2w = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 2w = 0 + -23
2w = 0 + -23

Combine like terms: 0 + -23 = -23
2w = -23

Divide each side by '2'.
w = -11.5

Simplifying
w = -11.5
Solution
w = {2, -11.5}