(3y-2)(2y)=66

Solution for (3y-2)(2y)=66 equation:

Simplifying
(3y + -2)(2y) = 66

Reorder the terms:
(-2 + 3y)(2y) = 66

Remove parenthesis around (2y)
(-2 + 3y) * 2y = 66

Reorder the terms for easier multiplication:
2y(-2 + 3y) = 66
(-2 * 2y + 3y * 2y) = 66
(-4y + 6y2) = 66

Solving
-4y + 6y2 = 66

Solving for variable 'y'.

Reorder the terms:
-66 + -4y + 6y2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + -4y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -2y + 3y2) = 0

Factor a trinomial.
2((-3 + -1y)(11 + -3y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
Subproblem 2
Set the factor '(11 + -3y)' equal to zero and attempt to solve:

Simplifying
11 + -3y = 0

Solving
11 + -3y = 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 + -3y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3y = 0 + -11
-3y = 0 + -11

Combine like terms: 0 + -11 = -11
-3y = -11

Divide each side by '-3'.
y = 3.666666667

Simplifying
y = 3.666666667
Solution
y = {-3, 3.666666667}