4x(3x-8)(2x+5)=0

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Solution for 4x(3x-8)(2x+5)=0 equation: 


Simplifying
4x(3x + -8)(2x + 5) = 0

Reorder the terms:
4x(-8 + 3x)(2x + 5) = 0

Reorder the terms:
4x(-8 + 3x)(5 + 2x) = 0

Multiply (-8 + 3x) * (5 + 2x)
4x(-8(5 + 2x) + 3x * (5 + 2x)) = 0
4x((5 * -8 + 2x * -8) + 3x * (5 + 2x)) = 0
4x((-40 + -16x) + 3x * (5 + 2x)) = 0
4x(-40 + -16x + (5 * 3x + 2x * 3x)) = 0
4x(-40 + -16x + (15x + 6x2)) = 0

Combine like terms: -16x + 15x = -1x
4x(-40 + -1x + 6x2) = 0
(-40 * 4x + -1x * 4x + 6x2 * 4x) = 0
(-160x + -4x2 + 24x3) = 0

Solving
-160x + -4x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-40 + -1x + 6x2) = 0

Factor a trinomial.
4x((-5 + -2x)(8 + -3x)) = 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 '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 3
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
Solution
x = {0, -2.5, 2.666666667}

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