(6x^3+x^2-4x)(4xy)=0

Solution for (6x^3+x^2-4x)(4xy)=0 equation:

Simplifying
(6x3 + x2 + -4x)(4xy) = 0

Reorder the terms:
(-4x + x2 + 6x3)(4xy) = 0

Remove parenthesis around (4xy)
(-4x + x2 + 6x3) * 4xy = 0

Reorder the terms for easier multiplication:
4xy(-4x + x2 + 6x3) = 0
(-4x * 4xy + x2 * 4xy + 6x3 * 4xy) = 0
(-16x2y + 4x3y + 24x4y) = 0

Solving
-16x2y + 4x3y + 24x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2y'.
4x2y(-4 + x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 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 '(-4 + x + 6x2)' equal to zero and attempt to solve:

Simplifying
-4 + x + 6x2 = 0

Solving
-4 + x + 6x2 = 0

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

Divide each side by '6'.
-0.6666666667 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.1666666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.1666666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.1666666667x + x2 = 0 + 0.6666666667
0.1666666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.1666666667x + x2 = 0.6666666667

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

Add '0.25' to each side of the equation.
0.1666666667x + 0.25 + x2 = 0.6666666667 + 0.25

Reorder the terms:
0.25 + 0.1666666667x + x2 = 0.6666666667 + 0.25

Combine like terms: 0.6666666667 + 0.25 = 0.9166666667
0.25 + 0.1666666667x + x2 = 0.9166666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.9166666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.957427108 and -0.957427108.

Subproblem 1
x + 0.5 = 0.957427108

Simplifying
x + 0.5 = 0.957427108

Reorder the terms:
0.5 + x = 0.957427108

Solving
0.5 + x = 0.957427108

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.957427108 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.957427108 + -0.5
x = 0.957427108 + -0.5

Combine like terms: 0.957427108 + -0.5 = 0.457427108
x = 0.457427108

Simplifying
x = 0.457427108

Subproblem 2
x + 0.5 = -0.957427108

Simplifying
x + 0.5 = -0.957427108

Reorder the terms:
0.5 + x = -0.957427108

Solving
0.5 + x = -0.957427108

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.957427108 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.957427108 + -0.5
x = -0.957427108 + -0.5

Combine like terms: -0.957427108 + -0.5 = -1.457427108
x = -1.457427108

Simplifying
x = -1.457427108

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.457427108, -1.457427108}
Solution
x = {0.457427108, -1.457427108}