3y^3+15y^2=18y

Solution for 3y^3+15y^2=18y equation:

Simplifying
3y3 + 15y2 = 18y

Reorder the terms:
15y2 + 3y3 = 18y

Solving
15y2 + 3y3 = 18y

Solving for variable 'y'.

Reorder the terms:
-18y + 15y2 + 3y3 = 18y + -18y

Combine like terms: 18y + -18y = 0
-18y + 15y2 + 3y3 = 0

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

Factor a trinomial.
3y((-6 + -1y)(1 + -1y)) = 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 '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 3
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
Solution
y = {0, -6, 1}