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

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


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

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

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

Multiply (8 + 3x) * (-8 + x)
2x(8(-8 + x) + 3x * (-8 + x)) = 0
2x((-8 * 8 + x * 8) + 3x * (-8 + x)) = 0
2x((-64 + 8x) + 3x * (-8 + x)) = 0
2x(-64 + 8x + (-8 * 3x + x * 3x)) = 0
2x(-64 + 8x + (-24x + 3x2)) = 0

Combine like terms: 8x + -24x = -16x
2x(-64 + -16x + 3x2) = 0
(-64 * 2x + -16x * 2x + 3x2 * 2x) = 0
(-128x + -32x2 + 6x3) = 0

Solving
-128x + -32x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-64 + -16x + 3x2) = 0

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

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 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 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, -2.666666667, 8}

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