2x^4+9x^3=-9x^2

Solution for 2x^4+9x^3=-9x^2 equation:

Simplifying
2x4 + 9x3 = -9x2

Reorder the terms:
9x3 + 2x4 = -9x2

Solving
9x3 + 2x4 = -9x2

Solving for variable 'x'.

Reorder the terms:
9x2 + 9x3 + 2x4 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
9x2 + 9x3 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(9 + 9x + 2x2) = 0

Factor a trinomial.
x2((3 + x)(3 + 2x)) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

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

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

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

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

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {0, -3, -1.5}