=8x^7-12x^5+4x^3

Solution for =8x^7-12x^5+4x^3 equation:

Simplifying
0 = 8x7 + -12x5 + 4x3

Reorder the terms:
0 = 4x3 + -12x5 + 8x7

Solving
0 = 4x3 + -12x5 + 8x7

Solving for variable 'x'.
Remove the zero:
-4x3 + 12x5 + -8x7 = 4x3 + -12x5 + 8x7 + -4x3 + 12x5 + -8x7

Reorder the terms:
-4x3 + 12x5 + -8x7 = 4x3 + -4x3 + -12x5 + 12x5 + 8x7 + -8x7

Combine like terms: 4x3 + -4x3 = 0
-4x3 + 12x5 + -8x7 = 0 + -12x5 + 12x5 + 8x7 + -8x7
-4x3 + 12x5 + -8x7 = -12x5 + 12x5 + 8x7 + -8x7

Combine like terms: -12x5 + 12x5 = 0
-4x3 + 12x5 + -8x7 = 0 + 8x7 + -8x7
-4x3 + 12x5 + -8x7 = 8x7 + -8x7

Combine like terms: 8x7 + -8x7 = 0
-4x3 + 12x5 + -8x7 = 0

Factor out the Greatest Common Factor (GCF), '4x3'.
4x3(-1 + 3x2 + -2x4) = 0

Factor a trinomial.
4x3((-1 + x2)(1 + -2x2)) = 0

Factor a difference between two squares.
4x3(((1 + x)(-1 + x))(1 + -2x2)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 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 + -2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x2 = 0 + -1
-2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x2 = -1

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Subproblem 4
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {-0.707106781, 0.707106781, -1, 1}