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

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

Simplifying
6(y + -3)(2y + -1) = 0

Reorder the terms:
6(-3 + y)(2y + -1) = 0

Reorder the terms:
6(-3 + y)(-1 + 2y) = 0

Multiply (-3 + y) * (-1 + 2y)
6(-3(-1 + 2y) + y(-1 + 2y)) = 0
6((-1 * -3 + 2y * -3) + y(-1 + 2y)) = 0
6((3 + -6y) + y(-1 + 2y)) = 0
6(3 + -6y + (-1 * y + 2y * y)) = 0
6(3 + -6y + (-1y + 2y2)) = 0

Combine like terms: -6y + -1y = -7y
6(3 + -7y + 2y2) = 0
(3 * 6 + -7y * 6 + 2y2 * 6) = 0
(18 + -42y + 12y2) = 0

Solving
18 + -42y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -7y + 2y2) = 0

Factor a trinomial.
6((1 + -2y)(3 + -1y)) = 0

Ignore the factor 6.
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 + -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
Solution
y = {0.5, 3}