9y^3+30y^2=3y^4

Solution for 9y^3+30y^2=3y^4 equation:

Simplifying
9y3 + 30y2 = 3y4

Reorder the terms:
30y2 + 9y3 = 3y4

Solving
30y2 + 9y3 = 3y4

Solving for variable 'y'.

Combine like terms: 3y4 + -3y4 = 0
30y2 + 9y3 + -3y4 = 0

Factor out the Greatest Common Factor (GCF), '3y2'.
3y2(10 + 3y + -1y2) = 0

Factor a trinomial.
3y2((5 + -1y)(2 + y)) = 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 '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Subproblem 3
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2
Solution
y = {0, 5, -2}