x=-(x^4+9x^2-6x^3)+3(-x^2+3x)

Solution for x=-(x^4+9x^2-6x^3)+3(-x^2+3x) equation:

Simplifying
x = -1(x4 + 9x2 + -6x3) + 3(-1x2 + 3x)

Reorder the terms:
x = -1(9x2 + -6x3 + x4) + 3(-1x2 + 3x)
x = (9x2 * -1 + -6x3 * -1 + x4 * -1) + 3(-1x2 + 3x)
x = (-9x2 + 6x3 + -1x4) + 3(-1x2 + 3x)

Reorder the terms:
x = -9x2 + 6x3 + -1x4 + 3(3x + -1x2)
x = -9x2 + 6x3 + -1x4 + (3x * 3 + -1x2 * 3)
x = -9x2 + 6x3 + -1x4 + (9x + -3x2)

Reorder the terms:
x = 9x + -9x2 + -3x2 + 6x3 + -1x4

Combine like terms: -9x2 + -3x2 = -12x2
x = 9x + -12x2 + 6x3 + -1x4

Solving
x = 9x + -12x2 + 6x3 + -1x4

Solving for variable 'x'.

Combine like terms: x + -9x = -8x
-8x + 12x2 + -6x3 + x4 = 9x + -12x2 + 6x3 + -1x4 + -9x + 12x2 + -6x3 + x4

Reorder the terms:
-8x + 12x2 + -6x3 + x4 = 9x + -9x + -12x2 + 12x2 + 6x3 + -6x3 + -1x4 + x4

Combine like terms: 9x + -9x = 0
-8x + 12x2 + -6x3 + x4 = 0 + -12x2 + 12x2 + 6x3 + -6x3 + -1x4 + x4
-8x + 12x2 + -6x3 + x4 = -12x2 + 12x2 + 6x3 + -6x3 + -1x4 + x4

Combine like terms: -12x2 + 12x2 = 0
-8x + 12x2 + -6x3 + x4 = 0 + 6x3 + -6x3 + -1x4 + x4
-8x + 12x2 + -6x3 + x4 = 6x3 + -6x3 + -1x4 + x4

Combine like terms: 6x3 + -6x3 = 0
-8x + 12x2 + -6x3 + x4 = 0 + -1x4 + x4
-8x + 12x2 + -6x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
-8x + 12x2 + -6x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + 12x + -6x2 + x3) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-8 + 12x + -6x2 + x3)' equal to zero and attempt to solve:

Simplifying
-8 + 12x + -6x2 + x3 = 0

Solving
-8 + 12x + -6x2 + x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}