4x(x-3)(x+8)=2x^3-24x+10x^2

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Solution for 4x(x-3)(x+8)=2x^3-24x+10x^2 equation: 


Simplifying
4x(x + -3)(x + 8) = 2x3 + -24x + 10x2

Reorder the terms:
4x(-3 + x)(x + 8) = 2x3 + -24x + 10x2

Reorder the terms:
4x(-3 + x)(8 + x) = 2x3 + -24x + 10x2

Multiply (-3 + x) * (8 + x)
4x(-3(8 + x) + x(8 + x)) = 2x3 + -24x + 10x2
4x((8 * -3 + x * -3) + x(8 + x)) = 2x3 + -24x + 10x2
4x((-24 + -3x) + x(8 + x)) = 2x3 + -24x + 10x2
4x(-24 + -3x + (8 * x + x * x)) = 2x3 + -24x + 10x2
4x(-24 + -3x + (8x + x2)) = 2x3 + -24x + 10x2

Combine like terms: -3x + 8x = 5x
4x(-24 + 5x + x2) = 2x3 + -24x + 10x2
(-24 * 4x + 5x * 4x + x2 * 4x) = 2x3 + -24x + 10x2
(-96x + 20x2 + 4x3) = 2x3 + -24x + 10x2

Reorder the terms:
-96x + 20x2 + 4x3 = -24x + 10x2 + 2x3

Solving
-96x + 20x2 + 4x3 = -24x + 10x2 + 2x3

Solving for variable 'x'.

Reorder the terms:
-96x + 24x + 20x2 + -10x2 + 4x3 + -2x3 = -24x + 10x2 + 2x3 + 24x + -10x2 + -2x3

Combine like terms: -96x + 24x = -72x
-72x + 20x2 + -10x2 + 4x3 + -2x3 = -24x + 10x2 + 2x3 + 24x + -10x2 + -2x3

Combine like terms: 20x2 + -10x2 = 10x2
-72x + 10x2 + 4x3 + -2x3 = -24x + 10x2 + 2x3 + 24x + -10x2 + -2x3

Combine like terms: 4x3 + -2x3 = 2x3
-72x + 10x2 + 2x3 = -24x + 10x2 + 2x3 + 24x + -10x2 + -2x3

Reorder the terms:
-72x + 10x2 + 2x3 = -24x + 24x + 10x2 + -10x2 + 2x3 + -2x3

Combine like terms: -24x + 24x = 0
-72x + 10x2 + 2x3 = 0 + 10x2 + -10x2 + 2x3 + -2x3
-72x + 10x2 + 2x3 = 10x2 + -10x2 + 2x3 + -2x3

Combine like terms: 10x2 + -10x2 = 0
-72x + 10x2 + 2x3 = 0 + 2x3 + -2x3
-72x + 10x2 + 2x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-72x + 10x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-36 + 5x + x2) = 0

Factor a trinomial.
2x((-9 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

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 '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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, -9, 4}

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