(3x)(5x^2-4x+6)(-4)=0

Solution for (3x)(5x^2-4x+6)(-4)=0 equation:

Simplifying
(3x)(5x2 + -4x + 6)(-4) = 0

Remove parenthesis around (3x)
3x(5x2 + -4x + 6)(-4) = 0

Reorder the terms:
3x(6 + -4x + 5x2)(-4) = 0

Reorder the terms for easier multiplication:
3 * -4x(6 + -4x + 5x2) = 0

Multiply 3 * -4
-12x(6 + -4x + 5x2) = 0
(6 * -12x + -4x * -12x + 5x2 * -12x) = 0
(-72x + 48x2 + -60x3) = 0

Solving
-72x + 48x2 + -60x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(-6 + 4x + -5x2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-6 + 4x + -5x2)' equal to zero and attempt to solve:

Simplifying
-6 + 4x + -5x2 = 0

Solving
-6 + 4x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
1.2 + -0.8x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -0.8x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -0.8x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -0.8x + x2 = 0 + -1.2
-0.8x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-0.8x + x2 = -1.2

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = -1.2 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = -1.2 + 0.16

Combine like terms: -1.2 + 0.16 = -1.04
0.16 + -0.8x + x2 = -1.04

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = -1.04

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}