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

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


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

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

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

Multiply (-2 + x) * (5 + 3x)
-1x(-2(5 + 3x) + x(5 + 3x)) = 0
-1x((5 * -2 + 3x * -2) + x(5 + 3x)) = 0
-1x((-10 + -6x) + x(5 + 3x)) = 0
-1x(-10 + -6x + (5 * x + 3x * x)) = 0
-1x(-10 + -6x + (5x + 3x2)) = 0

Combine like terms: -6x + 5x = -1x
-1x(-10 + -1x + 3x2) = 0
(-10 * -1x + -1x * -1x + 3x2 * -1x) = 0
(10x + 1x2 + -3x3) = 0

Solving
10x + 1x2 + -3x3 = 0

Solving for variable 'x'.

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

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


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 + -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

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

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {0, 2, -1.666666667}

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