3y^3+36y^2=3y^4

Solution for 3y^3+36y^2=3y^4 equation:

Simplifying
3y3 + 36y2 = 3y4

Reorder the terms:
36y2 + 3y3 = 3y4

Solving
36y2 + 3y3 = 3y4

Solving for variable 'y'.

Combine like terms: 3y4 + -3y4 = 0
36y2 + 3y3 + -3y4 = 0

Factor out the Greatest Common Factor (GCF), '3y2'.
3y2(12 + y + -1y2) = 0

Factor a trinomial.
3y2((4 + -1y)(3 + 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 '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

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

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3
Solution
y = {0, 4, -3}