8x^3(4x^2+7x-1)=0

Solution for 8x^3(4x^2+7x-1)=0 equation:

Simplifying
8x3(4x2 + 7x + -1) = 0

Reorder the terms:
8x3(-1 + 7x + 4x2) = 0
(-1 * 8x3 + 7x * 8x3 + 4x2 * 8x3) = 0
(-8x3 + 56x4 + 32x5) = 0

Solving
-8x3 + 56x4 + 32x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x3'.
8x3(-1 + 7x + 4x2) = 0

Ignore the factor 8.
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 + 7x + 4x2)' equal to zero and attempt to solve:

Simplifying
-1 + 7x + 4x2 = 0

Solving
-1 + 7x + 4x2 = 0

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

Divide each side by '4'.
-0.25 + 1.75x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 1.75x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 1.75x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 1.75x + x2 = 0 + 0.25
1.75x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
1.75x + x2 = 0.25

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 0.25 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 0.25 + 0.765625

Combine like terms: 0.25 + 0.765625 = 1.015625
0.765625 + 1.75x + x2 = 1.015625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + 0.875) equal to 1.007782219 and -1.007782219.

Subproblem 1
x + 0.875 = 1.007782219

Simplifying
x + 0.875 = 1.007782219

Reorder the terms:
0.875 + x = 1.007782219

Solving
0.875 + x = 1.007782219

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = 1.007782219 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = 1.007782219 + -0.875
x = 1.007782219 + -0.875

Combine like terms: 1.007782219 + -0.875 = 0.132782219
x = 0.132782219

Simplifying
x = 0.132782219

Subproblem 2
x + 0.875 = -1.007782219

Simplifying
x + 0.875 = -1.007782219

Reorder the terms:
0.875 + x = -1.007782219

Solving
0.875 + x = -1.007782219

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = -1.007782219 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = -1.007782219 + -0.875
x = -1.007782219 + -0.875

Combine like terms: -1.007782219 + -0.875 = -1.882782219
x = -1.882782219

Simplifying
x = -1.882782219

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.132782219, -1.882782219}
Solution
x = {0.132782219, -1.882782219}