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

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


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

Reorder the terms:
2x(-3 + x)(4x + 8) = 0

Reorder the terms:
2x(-3 + x)(8 + 4x) = 0

Multiply (-3 + x) * (8 + 4x)
2x(-3(8 + 4x) + x(8 + 4x)) = 0
2x((8 * -3 + 4x * -3) + x(8 + 4x)) = 0
2x((-24 + -12x) + x(8 + 4x)) = 0
2x(-24 + -12x + (8 * x + 4x * x)) = 0
2x(-24 + -12x + (8x + 4x2)) = 0

Combine like terms: -12x + 8x = -4x
2x(-24 + -4x + 4x2) = 0
(-24 * 2x + -4x * 2x + 4x2 * 2x) = 0
(-48x + -8x2 + 8x3) = 0

Solving
-48x + -8x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(-6 + -1x + x2) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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

Simplifying
3 + -1x = 0

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

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -2, 3}

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