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

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


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

Reorder the terms:
3x(-4 + 6x + -5x2) = 0
(-4 * 3x + 6x * 3x + -5x2 * 3x) = 0
(-12x + 18x2 + -15x3) = 0

Solving
-12x + 18x2 + -15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + 6x + -5x2) = 0

Ignore the factor 3.

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 '(-4 + 6x + -5x2)' equal to zero and attempt to solve:

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

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

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

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

Move the constant term to the right:

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

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

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

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

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = -0.8 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = -0.8 + 0.36

Combine like terms: -0.8 + 0.36 = -0.44
0.36 + -1.2x + x2 = -0.44

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = -0.44

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}

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