=8x^6-40x^5+48x^4-24x^2

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Solution for =8x^6-40x^5+48x^4-24x^2 equation: 


Simplifying
0 = 8x6 + -40x5 + 48x4 + -24x2

Reorder the terms:
0 = -24x2 + 48x4 + -40x5 + 8x6

Solving
0 = -24x2 + 48x4 + -40x5 + 8x6

Solving for variable 'x'.
Remove the zero:
24x2 + -48x4 + 40x5 + -8x6 = -24x2 + 48x4 + -40x5 + 8x6 + 24x2 + -48x4 + 40x5 + -8x6

Reorder the terms:
24x2 + -48x4 + 40x5 + -8x6 = -24x2 + 24x2 + 48x4 + -48x4 + -40x5 + 40x5 + 8x6 + -8x6

Combine like terms: -24x2 + 24x2 = 0
24x2 + -48x4 + 40x5 + -8x6 = 0 + 48x4 + -48x4 + -40x5 + 40x5 + 8x6 + -8x6
24x2 + -48x4 + 40x5 + -8x6 = 48x4 + -48x4 + -40x5 + 40x5 + 8x6 + -8x6

Combine like terms: 48x4 + -48x4 = 0
24x2 + -48x4 + 40x5 + -8x6 = 0 + -40x5 + 40x5 + 8x6 + -8x6
24x2 + -48x4 + 40x5 + -8x6 = -40x5 + 40x5 + 8x6 + -8x6

Combine like terms: -40x5 + 40x5 = 0
24x2 + -48x4 + 40x5 + -8x6 = 0 + 8x6 + -8x6
24x2 + -48x4 + 40x5 + -8x6 = 8x6 + -8x6

Combine like terms: 8x6 + -8x6 = 0
24x2 + -48x4 + 40x5 + -8x6 = 0

Factor out the Greatest Common Factor (GCF), '8x2'.
8x2(3 + -6x2 + 5x3 + -1x4) = 0

Ignore the factor 8.

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 + -6x2 + 5x3 + -1x4)' equal to zero and attempt to solve:

Simplifying
3 + -6x2 + 5x3 + -1x4 = 0

Solving
3 + -6x2 + 5x3 + -1x4 = 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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