3x(4x-8)(x+5)=0

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Solution for 3x(4x-8)(x+5)=0 equation: 


Simplifying
3x(4x + -8)(x + 5) = 0

Reorder the terms:
3x(-8 + 4x)(x + 5) = 0

Reorder the terms:
3x(-8 + 4x)(5 + x) = 0

Multiply (-8 + 4x) * (5 + x)
3x(-8(5 + x) + 4x * (5 + x)) = 0
3x((5 * -8 + x * -8) + 4x * (5 + x)) = 0
3x((-40 + -8x) + 4x * (5 + x)) = 0
3x(-40 + -8x + (5 * 4x + x * 4x)) = 0
3x(-40 + -8x + (20x + 4x2)) = 0

Combine like terms: -8x + 20x = 12x
3x(-40 + 12x + 4x2) = 0
(-40 * 3x + 12x * 3x + 4x2 * 3x) = 0
(-120x + 36x2 + 12x3) = 0

Solving
-120x + 36x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(-10 + 3x + x2) = 0

Factor a trinomial.
12x((-5 + -1x)(2 + -1x)) = 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 '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 3
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
Solution
x = {0, -5, 2}

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