6x^4+15x^3=9x^2

Solution for 6x^4+15x^3=9x^2 equation:

Simplifying
6x4 + 15x3 = 9x2

Reorder the terms:
15x3 + 6x4 = 9x2

Solving
15x3 + 6x4 = 9x2

Solving for variable 'x'.

Reorder the terms:
-9x2 + 15x3 + 6x4 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-9x2 + 15x3 + 6x4 = 0

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-3 + 5x + 2x2) = 0

Factor a trinomial.
3x2((-3 + -1x)(1 + -2x)) = 0

Ignore the factor 3.
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 + -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
Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -3, 0.5}