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

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


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

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

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

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

Combine like terms: 7x + -1x = 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((-7 + -1x)(1 + -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 '(-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

Subproblem 3
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
Solution
x = {0, -7, 1}

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