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

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

Simplifying
3y2(2y + 3)(y + -3) = 0

Reorder the terms:
3y2(3 + 2y)(y + -3) = 0

Reorder the terms:
3y2(3 + 2y)(-3 + y) = 0

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

Combine like terms: 3y + -6y = -3y
3y2(-9 + -3y + 2y2) = 0
(-9 * 3y2 + -3y * 3y2 + 2y2 * 3y2) = 0
(-27y2 + -9y3 + 6y4) = 0

Solving
-27y2 + -9y3 + 6y4 = 0

Solving for variable 'y'.

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

Factor a trinomial.
3y2((-3 + -2y)(3 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
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
Subproblem 3
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, -1.5, 3}