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

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


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

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

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

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

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

Solving
-7x + -6x2 + x3 = 0

Solving for variable 'x'.

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

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

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

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