(2+x)(6+x)=0

Solution for (2+x)(6+x)=0 equation:

Simplifying
(2 + x)(6 + x) = 0

Multiply (2 + x) * (6 + x)
(2(6 + x) + x(6 + x)) = 0
((6 * 2 + x * 2) + x(6 + x)) = 0
((12 + 2x) + x(6 + x)) = 0
(12 + 2x + (6 * x + x * x)) = 0
(12 + 2x + (6x + x2)) = 0

Combine like terms: 2x + 6x = 8x
(12 + 8x + x2) = 0

Solving
12 + 8x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + x)(2 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-6, -2}