(9x^4-6x^2+1)-(x^4-12x^3+34x^2+12x+1)=0

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Solution for (9x^4-6x^2+1)-(x^4-12x^3+34x^2+12x+1)=0 equation: 


Simplifying
(9x4 + -6x2 + 1) + -1(x4 + -12x3 + 34x2 + 12x + 1) = 0

Reorder the terms:
(1 + -6x2 + 9x4) + -1(x4 + -12x3 + 34x2 + 12x + 1) = 0

Remove parenthesis around (1 + -6x2 + 9x4)
1 + -6x2 + 9x4 + -1(x4 + -12x3 + 34x2 + 12x + 1) = 0

Reorder the terms:
1 + -6x2 + 9x4 + -1(1 + 12x + 34x2 + -12x3 + x4) = 0
1 + -6x2 + 9x4 + (1 * -1 + 12x * -1 + 34x2 * -1 + -12x3 * -1 + x4 * -1) = 0
1 + -6x2 + 9x4 + (-1 + -12x + -34x2 + 12x3 + -1x4) = 0

Reorder the terms:
1 + -1 + -12x + -6x2 + -34x2 + 12x3 + 9x4 + -1x4 = 0

Combine like terms: 1 + -1 = 0
0 + -12x + -6x2 + -34x2 + 12x3 + 9x4 + -1x4 = 0
-12x + -6x2 + -34x2 + 12x3 + 9x4 + -1x4 = 0

Combine like terms: -6x2 + -34x2 = -40x2
-12x + -40x2 + 12x3 + 9x4 + -1x4 = 0

Combine like terms: 9x4 + -1x4 = 8x4
-12x + -40x2 + 12x3 + 8x4 = 0

Solving
-12x + -40x2 + 12x3 + 8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-3 + -10x + 3x2 + 2x3) = 0

Ignore the factor 4.

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 '(-3 + -10x + 3x2 + 2x3)' equal to zero and attempt to solve:

Simplifying
-3 + -10x + 3x2 + 2x3 = 0

Solving
-3 + -10x + 3x2 + 2x3 = 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}

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