x^2+10x+6=x+6

Solution for x^2+10x+6=x+6 equation:

Simplifying
x2 + 10x + 6 = x + 6

Reorder the terms:
6 + 10x + x2 = x + 6

Reorder the terms:
6 + 10x + x2 = 6 + x

Add '-6' to each side of the equation.
6 + 10x + -6 + x2 = 6 + -6 + x

Reorder the terms:
6 + -6 + 10x + x2 = 6 + -6 + x

Combine like terms: 6 + -6 = 0
0 + 10x + x2 = 6 + -6 + x
10x + x2 = 6 + -6 + x

Combine like terms: 6 + -6 = 0
10x + x2 = 0 + x
10x + x2 = x

Solving
10x + x2 = x

Solving for variable 'x'.

Reorder the terms:
10x + -1x + x2 = x + -1x

Combine like terms: 10x + -1x = 9x
9x + x2 = x + -1x

Combine like terms: x + -1x = 0
9x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + 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 '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {0, -9}