(x+2)(x+6)=x

Solution for (x+2)(x+6)=x equation:

Simplifying
(x + 2)(x + 6) = x

Reorder the terms:
(2 + x)(x + 6) = x

Reorder the terms:
(2 + x)(6 + x) = x

Multiply (2 + x) * (6 + x)
(2(6 + x) + x(6 + x)) = x
((6 * 2 + x * 2) + x(6 + x)) = x
((12 + 2x) + x(6 + x)) = x
(12 + 2x + (6 * x + x * x)) = x
(12 + 2x + (6x + x2)) = x

Combine like terms: 2x + 6x = 8x
(12 + 8x + x2) = x

Solving
12 + 8x + x2 = x

Solving for variable 'x'.

Reorder the terms:
12 + 8x + -1x + x2 = x + -1x

Combine like terms: 8x + -1x = 7x
12 + 7x + x2 = x + -1x

Combine like terms: x + -1x = 0
12 + 7x + x2 = 0

Factor a trinomial.
(4 + x)(3 + x) = 0

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-4, -3}