-4x^3(x^3+8x)+7x^6=

Solution for -4x^3(x^3+8x)+7x^6= equation:

Simplifying
-4x3(x3 + 8x) + 7x6 = 0

Reorder the terms:
-4x3(8x + x3) + 7x6 = 0
(8x * -4x3 + x3 * -4x3) + 7x6 = 0
(-32x4 + -4x6) + 7x6 = 0

Combine like terms: -4x6 + 7x6 = 3x6
-32x4 + 3x6 = 0

Solving
-32x4 + 3x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x4'.
x4(-32 + 3x2) = 0

Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve:

Simplifying
x4 = 0

Solving
x4 = 0

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

Simplifying
x4 = 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 '(-32 + 3x2)' equal to zero and attempt to solve:

Simplifying
-32 + 3x2 = 0

Solving
-32 + 3x2 = 0

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

Add '32' to each side of the equation.
-32 + 32 + 3x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 3x2 = 0 + 32
3x2 = 0 + 32

Combine like terms: 0 + 32 = 32
3x2 = 32

Divide each side by '3'.
x2 = 10.66666667

Simplifying
x2 = 10.66666667

Take the square root of each side:
x = {-3.265986324, 3.265986324}
Solution
x = {-3.265986324, 3.265986324}