x(x+8)=x

Solution for x(x+8)=x equation:

Simplifying
x(x + 8) = x

Reorder the terms:
x(8 + x) = x
(8 * x + x * x) = x
(8x + x2) = x

Solving
8x + x2 = x

Solving for variable 'x'.

Reorder the terms:
8x + -1x + x2 = x + -1x

Combine like terms: 8x + -1x = 7x
7x + x2 = x + -1x

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(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 '(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, -7}