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

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


Simplifying
8x(3 + -2x)(4 + -1x) = 0

Multiply (3 + -2x) * (4 + -1x)
8x(3(4 + -1x) + -2x * (4 + -1x)) = 0
8x((4 * 3 + -1x * 3) + -2x * (4 + -1x)) = 0
8x((12 + -3x) + -2x * (4 + -1x)) = 0
8x(12 + -3x + (4 * -2x + -1x * -2x)) = 0
8x(12 + -3x + (-8x + 2x2)) = 0

Combine like terms: -3x + -8x = -11x
8x(12 + -11x + 2x2) = 0
(12 * 8x + -11x * 8x + 2x2 * 8x) = 0
(96x + -88x2 + 16x3) = 0

Solving
96x + -88x2 + 16x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(12 + -11x + 2x2) = 0

Factor a trinomial.
8x((3 + -2x)(4 + -1x)) = 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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 1.5, 4}

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