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

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


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

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

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

Multiply (-8 + 3x) * (4 + 5x)
3x(-8(4 + 5x) + 3x * (4 + 5x)) = 0
3x((4 * -8 + 5x * -8) + 3x * (4 + 5x)) = 0
3x((-32 + -40x) + 3x * (4 + 5x)) = 0
3x(-32 + -40x + (4 * 3x + 5x * 3x)) = 0
3x(-32 + -40x + (12x + 15x2)) = 0

Combine like terms: -40x + 12x = -28x
3x(-32 + -28x + 15x2) = 0
(-32 * 3x + -28x * 3x + 15x2 * 3x) = 0
(-96x + -84x2 + 45x3) = 0

Solving
-96x + -84x2 + 45x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-32 + -28x + 15x2) = 0

Factor a trinomial.
3x((-4 + -5x)(8 + -3x)) = 0

Ignore the factor 3.

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 '(-4 + -5x)' equal to zero and attempt to solve:

Simplifying
-4 + -5x = 0

Solving
-4 + -5x = 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 + -5x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x = 0 + 4
-5x = 0 + 4

Combine like terms: 0 + 4 = 4
-5x = 4

Divide each side by '-5'.
x = -0.8

Simplifying
x = -0.8

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, -0.8, 2.666666667}

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