x(x+7)=x

Solution for x(x+7)=x equation:

Simplifying
x(x + 7) = x

Reorder the terms:
x(7 + x) = x
(7 * x + x * x) = x
(7x + x2) = x

Solving
7x + x2 = x

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {0, -6}