27y^3+15y^2-12y=0

Solution for 27y^3+15y^2-12y=0 equation:

Simplifying
27y3 + 15y2 + -12y = 0

Reorder the terms:
-12y + 15y2 + 27y3 = 0

Solving
-12y + 15y2 + 27y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-4 + 5y + 9y2) = 0

Factor a trinomial.
3y((-1 + -1y)(4 + -9y)) = 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 '(-1 + -1y)' equal to zero and attempt to solve:

Simplifying
-1 + -1y = 0

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

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

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

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

Simplifying
y = -1
Subproblem 3
Set the factor '(4 + -9y)' equal to zero and attempt to solve:

Simplifying
4 + -9y = 0

Solving
4 + -9y = 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 + -9y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9y = 0 + -4
-9y = 0 + -4

Combine like terms: 0 + -4 = -4
-9y = -4

Divide each side by '-9'.
y = 0.4444444444

Simplifying
y = 0.4444444444
Solution
y = {0, -1, 0.4444444444}