-8x^5(6x^3+3x^2-2x)=

Solution for -8x^5(6x^3+3x^2-2x)= equation:

Simplifying
-8x5(6x3 + 3x2 + -2x) = 0

Reorder the terms:
-8x5(-2x + 3x2 + 6x3) = 0
(-2x * -8x5 + 3x2 * -8x5 + 6x3 * -8x5) = 0
(16x6 + -24x7 + -48x8) = 0

Solving
16x6 + -24x7 + -48x8 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x6'.
8x6(2 + -3x + -6x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'x6' equal to zero and attempt to solve:

Simplifying
x6 = 0

Solving
x6 = 0

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

Simplifying
x6 = 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 '(2 + -3x + -6x2)' equal to zero and attempt to solve:

Simplifying
2 + -3x + -6x2 = 0

Solving
2 + -3x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.3333333333 + 0.5x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.5x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.5x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.5x + x2 = 0 + 0.3333333333
0.5x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.5x + x2 = 0.3333333333

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.3333333333 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.3333333333 + 0.0625

Combine like terms: 0.3333333333 + 0.0625 = 0.3958333333
0.0625 + 0.5x + x2 = 0.3958333333

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.3958333333

Calculate the square root of the right side: 0.62915287

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.62915287 and -0.62915287.

Subproblem 1
x + 0.25 = 0.62915287

Simplifying
x + 0.25 = 0.62915287

Reorder the terms:
0.25 + x = 0.62915287

Solving
0.25 + x = 0.62915287

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.62915287 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.62915287 + -0.25
x = 0.62915287 + -0.25

Combine like terms: 0.62915287 + -0.25 = 0.37915287
x = 0.37915287

Simplifying
x = 0.37915287

Subproblem 2
x + 0.25 = -0.62915287

Simplifying
x + 0.25 = -0.62915287

Reorder the terms:
0.25 + x = -0.62915287

Solving
0.25 + x = -0.62915287

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.62915287 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.62915287 + -0.25
x = -0.62915287 + -0.25

Combine like terms: -0.62915287 + -0.25 = -0.87915287
x = -0.87915287

Simplifying
x = -0.87915287

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.37915287, -0.87915287}
Solution
x = {0.37915287, -0.87915287}