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

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


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

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

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

Multiply (-2 + x) * (4 + 5x)
3x(-2(4 + 5x) + x(4 + 5x)) = 0
3x((4 * -2 + 5x * -2) + x(4 + 5x)) = 0
3x((-8 + -10x) + x(4 + 5x)) = 0
3x(-8 + -10x + (4 * x + 5x * x)) = 0
3x(-8 + -10x + (4x + 5x2)) = 0

Combine like terms: -10x + 4x = -6x
3x(-8 + -6x + 5x2) = 0
(-8 * 3x + -6x * 3x + 5x2 * 3x) = 0
(-24x + -18x2 + 15x3) = 0

Solving
-24x + -18x2 + 15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-8 + -6x + 5x2) = 0

Factor a trinomial.
3x((-4 + -5x)(2 + -1x)) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, -0.8, 2}

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