24x^8-21x^5-3x^2=0

Solution for 24x^8-21x^5-3x^2=0 equation:

Simplifying
24x8 + -21x5 + -3x2 = 0

Reorder the terms:
-3x2 + -21x5 + 24x8 = 0

Solving
-3x2 + -21x5 + 24x8 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-1 + -7x3 + 8x6) = 0

Factor a trinomial.
3x2((-1 + -8x3)(1 + -1x3)) = 0

Ignore the factor 3.
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 '(-1 + -8x3)' equal to zero and attempt to solve:

Simplifying
-1 + -8x3 = 0

Solving
-1 + -8x3 = 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 + -8x3 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8x3 = 0 + 1
-8x3 = 0 + 1

Combine like terms: 0 + 1 = 1
-8x3 = 1

Divide each side by '-8'.
x3 = -0.125

Simplifying
x3 = -0.125

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}