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

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


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

Remove parenthesis around (2x)
2x(3x + 2)(x + -5) = 0

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

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

Multiply (2 + 3x) * (-5 + x)
2x(2(-5 + x) + 3x * (-5 + x)) = 0
2x((-5 * 2 + x * 2) + 3x * (-5 + x)) = 0
2x((-10 + 2x) + 3x * (-5 + x)) = 0
2x(-10 + 2x + (-5 * 3x + x * 3x)) = 0
2x(-10 + 2x + (-15x + 3x2)) = 0

Combine like terms: 2x + -15x = -13x
2x(-10 + -13x + 3x2) = 0
(-10 * 2x + -13x * 2x + 3x2 * 2x) = 0
(-20x + -26x2 + 6x3) = 0

Solving
-20x + -26x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-10 + -13x + 3x2) = 0

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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, -0.6666666667, 5}

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