w(2w+1)=66

Solution for w(2w+1)=66 equation:

Simplifying
w(2w + 1) = 66

Reorder the terms:
w(1 + 2w) = 66
(1 * w + 2w * w) = 66
(1w + 2w2) = 66

Solving
1w + 2w2 = 66

Solving for variable 'w'.

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

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

Factor a trinomial.
(-6 + -1w)(11 + -2w) = 0

Subproblem 1
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
Subproblem 2
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
Solution
w = {-6, 5.5}