-8u^3(7u^3+6u^2-8u)=

Solution for -8u^3(7u^3+6u^2-8u)= equation:

Simplifying
-8u3(7u3 + 6u2 + -8u) = 0

Reorder the terms:
-8u3(-8u + 6u2 + 7u3) = 0
(-8u * -8u3 + 6u2 * -8u3 + 7u3 * -8u3) = 0
(64u4 + -48u5 + -56u6) = 0

Solving
64u4 + -48u5 + -56u6 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '8u4'.
8u4(8 + -6u + -7u2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'u4' equal to zero and attempt to solve:

Simplifying
u4 = 0

Solving
u4 = 0

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

Simplifying
u4 = 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 '(8 + -6u + -7u2)' equal to zero and attempt to solve:

Simplifying
8 + -6u + -7u2 = 0

Solving
8 + -6u + -7u2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-1.142857143 + 0.8571428571u + u2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + 0.8571428571u + 1.142857143 + u2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + 0.8571428571u + u2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + 0.8571428571u + u2 = 0 + 1.142857143
0.8571428571u + u2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
0.8571428571u + u2 = 1.142857143

The u term is 0.8571428571u.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571u + 0.1836734694 + u2 = 1.142857143 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571u + u2 = 1.142857143 + 0.1836734694

Combine like terms: 1.142857143 + 0.1836734694 = 1.3265306124
0.1836734694 + 0.8571428571u + u2 = 1.3265306124

Factor a perfect square on the left side:
(u + 0.4285714286)(u + 0.4285714286) = 1.3265306124

Calculate the square root of the right side: 1.151751107

Break this problem into two subproblems by setting 
(u + 0.4285714286) equal to 1.151751107 and -1.151751107.

Subproblem 1
u + 0.4285714286 = 1.151751107

Simplifying
u + 0.4285714286 = 1.151751107

Reorder the terms:
0.4285714286 + u = 1.151751107

Solving
0.4285714286 + u = 1.151751107

Solving for variable 'u'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + u = 1.151751107 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + u = 1.151751107 + -0.4285714286
u = 1.151751107 + -0.4285714286

Combine like terms: 1.151751107 + -0.4285714286 = 0.7231796784
u = 0.7231796784

Simplifying
u = 0.7231796784

Subproblem 2
u + 0.4285714286 = -1.151751107

Simplifying
u + 0.4285714286 = -1.151751107

Reorder the terms:
0.4285714286 + u = -1.151751107

Solving
0.4285714286 + u = -1.151751107

Solving for variable 'u'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + u = -1.151751107 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + u = -1.151751107 + -0.4285714286
u = -1.151751107 + -0.4285714286

Combine like terms: -1.151751107 + -0.4285714286 = -1.5803225356
u = -1.5803225356

Simplifying
u = -1.5803225356

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.7231796784, -1.5803225356}
Solution
u = {0.7231796784, -1.5803225356}