9y^4+24y^3+12y^2=0

Solution for 9y^4+24y^3+12y^2=0 equation:

Simplifying
9y4 + 24y3 + 12y2 = 0

Reorder the terms:
12y2 + 24y3 + 9y4 = 0

Solving
12y2 + 24y3 + 9y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y2'.
3y2(4 + 8y + 3y2) = 0

Factor a trinomial.
3y2((2 + y)(2 + 3y)) = 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 '(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
Subproblem 3
Set the factor '(2 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

Solving
2 + 3y = 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 + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {0, -2, -0.6666666667}