5x(3x-1)(4x+2)=0

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Solution for 5x(3x-1)(4x+2)=0 equation: 


Simplifying
5x(3x + -1)(4x + 2) = 0

Reorder the terms:
5x(-1 + 3x)(4x + 2) = 0

Reorder the terms:
5x(-1 + 3x)(2 + 4x) = 0

Multiply (-1 + 3x) * (2 + 4x)
5x(-1(2 + 4x) + 3x * (2 + 4x)) = 0
5x((2 * -1 + 4x * -1) + 3x * (2 + 4x)) = 0
5x((-2 + -4x) + 3x * (2 + 4x)) = 0
5x(-2 + -4x + (2 * 3x + 4x * 3x)) = 0
5x(-2 + -4x + (6x + 12x2)) = 0

Combine like terms: -4x + 6x = 2x
5x(-2 + 2x + 12x2) = 0
(-2 * 5x + 2x * 5x + 12x2 * 5x) = 0
(-10x + 10x2 + 60x3) = 0

Solving
-10x + 10x2 + 60x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10x'.
10x(-1 + x + 6x2) = 0

Factor a trinomial.
10x((-1 + -2x)(1 + -3x)) = 0

Ignore the factor 10.

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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, -0.5, 0.3333333333}

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