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

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


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

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

Multiply (3 + -2x) * (8 + x)
4x(3(8 + x) + -2x * (8 + x)) = 0
4x((8 * 3 + x * 3) + -2x * (8 + x)) = 0
4x((24 + 3x) + -2x * (8 + x)) = 0
4x(24 + 3x + (8 * -2x + x * -2x)) = 0
4x(24 + 3x + (-16x + -2x2)) = 0

Combine like terms: 3x + -16x = -13x
4x(24 + -13x + -2x2) = 0
(24 * 4x + -13x * 4x + -2x2 * 4x) = 0
(96x + -52x2 + -8x3) = 0

Solving
96x + -52x2 + -8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(24 + -13x + -2x2) = 0

Factor a trinomial.
4x((3 + -2x)(8 + x)) = 0

Ignore the factor 4.

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 '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {0, 1.5, -8}

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