6y(2y-1)-2(3y)=9

Solution for 6y(2y-1)-2(3y)=9 equation:

Simplifying
6y(2y + -1) + -2(3y) = 9

Reorder the terms:
6y(-1 + 2y) + -2(3y) = 9
(-1 * 6y + 2y * 6y) + -2(3y) = 9
(-6y + 12y2) + -2(3y) = 9

Remove parenthesis around (3y)
-6y + 12y2 + -2 * 3y = 9

Multiply -2 * 3
-6y + 12y2 + -6y = 9

Reorder the terms:
-6y + -6y + 12y2 = 9

Combine like terms: -6y + -6y = -12y
-12y + 12y2 = 9

Solving
-12y + 12y2 = 9

Solving for variable 'y'.

Reorder the terms:
-9 + -12y + 12y2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -12y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -4y + 4y2) = 0

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

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

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2y = 0 + 1

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

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

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 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 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-0.5, 1.5}