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

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


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

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

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

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

Combine like terms: 5x + -4x = 1x
6x(-10 + 1x + 2x2) = 0
(-10 * 6x + 1x * 6x + 2x2 * 6x) = 0
(-60x + 6x2 + 12x3) = 0

Solving
-60x + 6x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-10 + x + 2x2) = 0

Factor a trinomial.
6x((-5 + -2x)(2 + -1x)) = 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 '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

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

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

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

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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, -2.5, 2}

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