0=x(x+7)(x-1)

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Solution for 0=x(x+7)(x-1) equation: 


Simplifying
0 = x(x + 7)(x + -1)

Reorder the terms:
0 = x(7 + x)(x + -1)

Reorder the terms:
0 = x(7 + x)(-1 + x)

Multiply (7 + x) * (-1 + x)
0 = x(7(-1 + x) + x(-1 + x))
0 = x((-1 * 7 + x * 7) + x(-1 + x))
0 = x((-7 + 7x) + x(-1 + x))
0 = x(-7 + 7x + (-1 * x + x * x))
0 = x(-7 + 7x + (-1x + x2))

Combine like terms: 7x + -1x = 6x
0 = x(-7 + 6x + x2)
0 = (-7 * x + 6x * x + x2 * x)
0 = (-7x + 6x2 + x3)

Solving
0 = -7x + 6x2 + x3

Solving for variable 'x'.
Remove the zero:
7x + -6x2 + -1x3 = -7x + 6x2 + x3 + 7x + -6x2 + -1x3

Reorder the terms:
7x + -6x2 + -1x3 = -7x + 7x + 6x2 + -6x2 + x3 + -1x3

Combine like terms: -7x + 7x = 0
7x + -6x2 + -1x3 = 0 + 6x2 + -6x2 + x3 + -1x3
7x + -6x2 + -1x3 = 6x2 + -6x2 + x3 + -1x3

Combine like terms: 6x2 + -6x2 = 0
7x + -6x2 + -1x3 = 0 + x3 + -1x3
7x + -6x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
7x + -6x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -6x + -1x2) = 0

Factor a trinomial.
x((1 + -1x)(7 + 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 '(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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {0, 1, -7}

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