66=w+2w^2

Solution for 66=w+2w^2 equation:

Simplifying
66 = w + 2w2

Solving
66 = w + 2w2

Solving for variable 'w'.

Reorder the terms:
66 + -1w + -2w2 = w + -1w + 2w2 + -2w2

Combine like terms: w + -1w = 0
66 + -1w + -2w2 = 0 + 2w2 + -2w2
66 + -1w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
66 + -1w + -2w2 = 0

Factor a trinomial.
(11 + -2w)(6 + w) = 0

Subproblem 1
Set the factor '(11 + -2w)' equal to zero and attempt to solve:

Simplifying
11 + -2w = 0

Solving
11 + -2w = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2w = 0 + -11
-2w = 0 + -11

Combine like terms: 0 + -11 = -11
-2w = -11

Divide each side by '-2'.
w = 5.5

Simplifying
w = 5.5
Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 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 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Solution
w = {5.5, -6}