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

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


Simplifying
8x(-1x2 + 3x + -4) = 0

Reorder the terms:
8x(-4 + 3x + -1x2) = 0
(-4 * 8x + 3x * 8x + -1x2 * 8x) = 0
(-32x + 24x2 + -8x3) = 0

Solving
-32x + 24x2 + -8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(-4 + 3x + -1x2) = 0

Ignore the factor 8.

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 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + 3x + -1x2 = 0

Solving
-4 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4 + -3x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -3x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -3x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x + x2 = 0 + -4
-3x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3x + x2 = -4

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -4 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -4 + 2.25

Combine like terms: -4 + 2.25 = -1.75
2.25 + -3x + x2 = -1.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -1.75

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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