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

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

Simplifying
2x4 + -3x3 = 9x2

Reorder the terms:
-3x3 + 2x4 = 9x2

Solving
-3x3 + 2x4 = 9x2

Solving for variable 'x'.

Reorder the terms:
-9x2 + -3x3 + 2x4 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-9x2 + -3x3 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-9 + -3x + 2x2) = 0

Factor a trinomial.
x2((-3 + -2x)(3 + -1x)) = 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 + -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
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

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