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

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


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

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

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

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

Combine like terms: -3x + 2x = -1x
-5x(-2 + -1x + 3x2) = 0
(-2 * -5x + -1x * -5x + 3x2 * -5x) = 0
(10x + 5x2 + -15x3) = 0

Solving
10x + 5x2 + -15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(2 + x + -3x2) = 0

Factor a trinomial.
5x((1 + -1x)(2 + 3x)) = 0

Ignore the factor 5.

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 3
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
Solution
x = {0, 1, -0.6666666667}

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