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

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

Simplifying
(6 + -1x)(2 + x) = 0

Multiply (6 + -1x) * (2 + x)
(6(2 + x) + -1x * (2 + x)) = 0
((2 * 6 + x * 6) + -1x * (2 + x)) = 0
((12 + 6x) + -1x * (2 + x)) = 0
(12 + 6x + (2 * -1x + x * -1x)) = 0
(12 + 6x + (-2x + -1x2)) = 0

Combine like terms: 6x + -2x = 4x
(12 + 4x + -1x2) = 0

Solving
12 + 4x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

Divide each side by '-1'.
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}