0=x(x+5)(x-8)

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Solution for 0=x(x+5)(x-8) equation:


Simplifying
0 = x(x + 5)(x + -8)

Reorder the terms:
0 = x(5 + x)(x + -8)

Reorder the terms:
0 = x(5 + x)(-8 + x)

Multiply (5 + x) * (-8 + x)
0 = x(5(-8 + x) + x(-8 + x))
0 = x((-8 * 5 + x * 5) + x(-8 + x))
0 = x((-40 + 5x) + x(-8 + x))
0 = x(-40 + 5x + (-8 * x + x * x))
0 = x(-40 + 5x + (-8x + x2))

Combine like terms: 5x + -8x = -3x
0 = x(-40 + -3x + x2)
0 = (-40 * x + -3x * x + x2 * x)
0 = (-40x + -3x2 + x3)

Solving
0 = -40x + -3x2 + x3

Solving for variable 'x'.
Remove the zero:
40x + 3x2 + -1x3 = -40x + -3x2 + x3 + 40x + 3x2 + -1x3

Reorder the terms:
40x + 3x2 + -1x3 = -40x + 40x + -3x2 + 3x2 + x3 + -1x3

Combine like terms: -40x + 40x = 0
40x + 3x2 + -1x3 = 0 + -3x2 + 3x2 + x3 + -1x3
40x + 3x2 + -1x3 = -3x2 + 3x2 + x3 + -1x3

Combine like terms: -3x2 + 3x2 = 0
40x + 3x2 + -1x3 = 0 + x3 + -1x3
40x + 3x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
40x + 3x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(40 + 3x + -1x2) = 0

Factor a trinomial.
x((8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

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, 8, -5}

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