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

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

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

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

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

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

Multiply 3 * 2
6y(-1 + 3y) = 4
(-1 * 6y + 3y * 6y) = 4
(-6y + 18y2) = 4

Solving
-6y + 18y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + -6y + 18y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -6y + 18y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -3y + 9y2) = 0

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

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

Simplifying
-1 + -3y = 0

Solving
-1 + -3y = 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 + -3y = 0 + 1

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

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

Divide each side by '-3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Subproblem 2
Set the factor '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3y = 0 + -2

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

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

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {-0.3333333333, 0.6666666667}