x^8+63x^5-64x^2=0

Solution for x^8+63x^5-64x^2=0 equation:

Simplifying
x8 + 63x5 + -64x2 = 0

Reorder the terms:
-64x2 + 63x5 + x8 = 0

Solving
-64x2 + 63x5 + x8 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-64 + 63x3 + x6) = 0

Factor a trinomial.
x2((-64 + -1x3)(1 + -1x3)) = 0

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 '(-64 + -1x3)' equal to zero and attempt to solve:

Simplifying
-64 + -1x3 = 0

Solving
-64 + -1x3 = 0

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

Add '64' to each side of the equation.
-64 + 64 + -1x3 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -1x3 = 0 + 64
-1x3 = 0 + 64

Combine like terms: 0 + 64 = 64
-1x3 = 64

Divide each side by '-1'.
x3 = -64

Simplifying
x3 = -64

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + -1x3)' equal to zero and attempt to solve:

Simplifying
1 + -1x3 = 0

Solving
1 + -1x3 = 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 + -1x3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x3 = 0 + -1
-1x3 = 0 + -1

Combine like terms: 0 + -1 = -1
-1x3 = -1

Divide each side by '-1'.
x3 = 1

Simplifying
x3 = 1

The solution to this equation could not be determined.

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