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

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


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

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

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

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

Combine like terms: 16x + 3x = 19x
4x(24 + 19x + 2x2) = 0
(24 * 4x + 19x * 4x + 2x2 * 4x) = 0
(96x + 76x2 + 8x3) = 0

Solving
96x + 76x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(24 + 19x + 2x2) = 0

Factor a trinomial.
4x((8 + x)(3 + 2x)) = 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 '(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 '(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
Solution
x = {0, -8, -1.5}

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