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

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


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

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

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

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

Combine like terms: 24x + 2x = 26x
2x(16 + 26x + 3x2) = 0
(16 * 2x + 26x * 2x + 3x2 * 2x) = 0
(32x + 52x2 + 6x3) = 0

Solving
32x + 52x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(16 + 26x + 3x2) = 0

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

Subproblem 3
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -8, -0.6666666667}

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