4(3y-1)3(2y)=6

Solution for 4(3y-1)3(2y)=6 equation:

Simplifying
4(3y + -1) * 3(2y) = 6

Reorder the terms:
4(-1 + 3y) * 3(2y) = 6

Remove parenthesis around (2y)
4(-1 + 3y) * 3 * 2y = 6

Reorder the terms for easier multiplication:
4 * 3 * 2y(-1 + 3y) = 6

Multiply 4 * 3
12 * 2y(-1 + 3y) = 6

Multiply 12 * 2
24y(-1 + 3y) = 6
(-1 * 24y + 3y * 24y) = 6
(-24y + 72y2) = 6

Solving
-24y + 72y2 = 6

Solving for variable 'y'.

Reorder the terms:
-6 + -24y + 72y2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -24y + 72y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -4y + 12y2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -6y)' equal to zero and attempt to solve:

Simplifying
-1 + -6y = 0

Solving
-1 + -6y = 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 + -6y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6y = 0 + 1
-6y = 0 + 1

Combine like terms: 0 + 1 = 1
-6y = 1

Divide each side by '-6'.
y = -0.1666666667

Simplifying
y = -0.1666666667
Subproblem 2
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
Solution
y = {-0.1666666667, 0.5}