66=y(2y+1)

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

Simplifying
66 = y(2y + 1)

Reorder the terms:
66 = y(1 + 2y)
66 = (1 * y + 2y * y)
66 = (1y + 2y2)

Solving
66 = 1y + 2y2

Solving for variable 'y'.

Reorder the terms:
66 + -1y + -2y2 = 1y + -1y + 2y2 + -2y2

Combine like terms: 1y + -1y = 0
66 + -1y + -2y2 = 0 + 2y2 + -2y2
66 + -1y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
66 + -1y + -2y2 = 0

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

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

Simplifying
11 + -2y = 0

Solving
11 + -2y = 0

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

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

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

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

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

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

Simplifying
6 + y = 0

Solving
6 + y = 0

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

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

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

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

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