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

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


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

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

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

Multiply (-5 + 3x) * (2 + 4x)
x(-5(2 + 4x) + 3x * (2 + 4x)) = 0
x((2 * -5 + 4x * -5) + 3x * (2 + 4x)) = 0
x((-10 + -20x) + 3x * (2 + 4x)) = 0
x(-10 + -20x + (2 * 3x + 4x * 3x)) = 0
x(-10 + -20x + (6x + 12x2)) = 0

Combine like terms: -20x + 6x = -14x
x(-10 + -14x + 12x2) = 0
(-10 * x + -14x * x + 12x2 * x) = 0
(-10x + -14x2 + 12x3) = 0

Solving
-10x + -14x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-5 + -7x + 6x2) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 3
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, -0.5, 1.666666667}

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