0=6x(5x-2)(x+2)

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Solution for 0=6x(5x-2)(x+2) equation: 


Simplifying
0 = 6x(5x + -2)(x + 2)

Reorder the terms:
0 = 6x(-2 + 5x)(x + 2)

Reorder the terms:
0 = 6x(-2 + 5x)(2 + x)

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

Combine like terms: -2x + 10x = 8x
0 = 6x(-4 + 8x + 5x2)
0 = (-4 * 6x + 8x * 6x + 5x2 * 6x)
0 = (-24x + 48x2 + 30x3)

Solving
0 = -24x + 48x2 + 30x3

Solving for variable 'x'.
Remove the zero:
24x + -48x2 + -30x3 = -24x + 48x2 + 30x3 + 24x + -48x2 + -30x3

Reorder the terms:
24x + -48x2 + -30x3 = -24x + 24x + 48x2 + -48x2 + 30x3 + -30x3

Combine like terms: -24x + 24x = 0
24x + -48x2 + -30x3 = 0 + 48x2 + -48x2 + 30x3 + -30x3
24x + -48x2 + -30x3 = 48x2 + -48x2 + 30x3 + -30x3

Combine like terms: 48x2 + -48x2 = 0
24x + -48x2 + -30x3 = 0 + 30x3 + -30x3
24x + -48x2 + -30x3 = 30x3 + -30x3

Combine like terms: 30x3 + -30x3 = 0
24x + -48x2 + -30x3 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(4 + -8x + -5x2) = 0

Factor a trinomial.
6x((2 + -5x)(2 + x)) = 0

Ignore the factor 6.

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 '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

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

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

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {0, 0.4, -2}

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