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

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

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

Reorder the terms:
(6 + 2x)(6 + -1x) = 0

Multiply (6 + 2x) * (6 + -1x)
(6(6 + -1x) + 2x * (6 + -1x)) = 0
((6 * 6 + -1x * 6) + 2x * (6 + -1x)) = 0
((36 + -6x) + 2x * (6 + -1x)) = 0
(36 + -6x + (6 * 2x + -1x * 2x)) = 0
(36 + -6x + (12x + -2x2)) = 0

Combine like terms: -6x + 12x = 6x
(36 + 6x + -2x2) = 0

Solving
36 + 6x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 3x + -1x2) = 0

Factor a trinomial.
2((6 + -1x)(3 + x)) = 0

Ignore the factor 2.
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 '(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 = {6, -3}