66=x(2x+1)

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

Simplifying
66 = x(2x + 1)

Reorder the terms:
66 = x(1 + 2x)
66 = (1 * x + 2x * x)
66 = (1x + 2x2)

Solving
66 = 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
66 + -1x + -2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
66 + -1x + -2x2 = 0 + 2x2 + -2x2
66 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
66 + -1x + -2x2 = 0

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

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

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

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

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

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

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

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

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

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

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

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