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

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


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

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

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

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

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

Solving
0 = -10x + 3x2 + x3

Solving for variable 'x'.
Remove the zero:
10x + -3x2 + -1x3 = -10x + 3x2 + x3 + 10x + -3x2 + -1x3

Reorder the terms:
10x + -3x2 + -1x3 = -10x + 10x + 3x2 + -3x2 + x3 + -1x3

Combine like terms: -10x + 10x = 0
10x + -3x2 + -1x3 = 0 + 3x2 + -3x2 + x3 + -1x3
10x + -3x2 + -1x3 = 3x2 + -3x2 + x3 + -1x3

Combine like terms: 3x2 + -3x2 = 0
10x + -3x2 + -1x3 = 0 + x3 + -1x3
10x + -3x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
10x + -3x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + -3x + -1x2) = 0

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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5
Solution
x = {0, 2, -5}

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