3y^3(4y+3)(y-2)=

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

Simplifying
3y3(4y + 3)(y + -2) = 0

Reorder the terms:
3y3(3 + 4y)(y + -2) = 0

Reorder the terms:
3y3(3 + 4y)(-2 + y) = 0

Multiply (3 + 4y) * (-2 + y)
3y3(3(-2 + y) + 4y * (-2 + y)) = 0
3y3((-2 * 3 + y * 3) + 4y * (-2 + y)) = 0
3y3((-6 + 3y) + 4y * (-2 + y)) = 0
3y3(-6 + 3y + (-2 * 4y + y * 4y)) = 0
3y3(-6 + 3y + (-8y + 4y2)) = 0

Combine like terms: 3y + -8y = -5y
3y3(-6 + -5y + 4y2) = 0
(-6 * 3y3 + -5y * 3y3 + 4y2 * 3y3) = 0
(-18y3 + -15y4 + 12y5) = 0

Solving
-18y3 + -15y4 + 12y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y3'.
3y3(-6 + -5y + 4y2) = 0

Factor a trinomial.
3y3((-3 + -4y)(2 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve:

Simplifying
y3 = 0

Solving
y3 = 0

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

Simplifying
y3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-3 + -4y)' equal to zero and attempt to solve:

Simplifying
-3 + -4y = 0

Solving
-3 + -4y = 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 + -4y = 0 + 3

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

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

Divide each side by '-4'.
y = -0.75

Simplifying
y = -0.75
Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-0.75, 2}