3y(2y-3)(3y-4)=0

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Solution for 3y(2y-3)(3y-4)=0 equation: 


Simplifying
3y(2y + -3)(3y + -4) = 0

Reorder the terms:
3y(-3 + 2y)(3y + -4) = 0

Reorder the terms:
3y(-3 + 2y)(-4 + 3y) = 0

Multiply (-3 + 2y) * (-4 + 3y)
3y(-3(-4 + 3y) + 2y * (-4 + 3y)) = 0
3y((-4 * -3 + 3y * -3) + 2y * (-4 + 3y)) = 0
3y((12 + -9y) + 2y * (-4 + 3y)) = 0
3y(12 + -9y + (-4 * 2y + 3y * 2y)) = 0
3y(12 + -9y + (-8y + 6y2)) = 0

Combine like terms: -9y + -8y = -17y
3y(12 + -17y + 6y2) = 0
(12 * 3y + -17y * 3y + 6y2 * 3y) = 0
(36y + -51y2 + 18y3) = 0

Solving
36y + -51y2 + 18y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(12 + -17y + 6y2) = 0

Factor a trinomial.
3y((4 + -3y)(3 + -2y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(4 + -3y)' equal to zero and attempt to solve:

Simplifying
4 + -3y = 0

Solving
4 + -3y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3y = 0 + -4
-3y = 0 + -4

Combine like terms: 0 + -4 = -4
-3y = -4

Divide each side by '-3'.
y = 1.333333333

Simplifying
y = 1.333333333

Subproblem 3
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, 1.333333333, 1.5}

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