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

Solution for (3-x)(x+6)=0 equation:

Simplifying
(3 + -1x)(x + 6) = 0

Reorder the terms:
(3 + -1x)(6 + x) = 0

Multiply (3 + -1x) * (6 + x)
(3(6 + x) + -1x * (6 + x)) = 0
((6 * 3 + x * 3) + -1x * (6 + x)) = 0
((18 + 3x) + -1x * (6 + x)) = 0
(18 + 3x + (6 * -1x + x * -1x)) = 0
(18 + 3x + (-6x + -1x2)) = 0

Combine like terms: 3x + -6x = -3x
(18 + -3x + -1x2) = 0

Solving
18 + -3x + -1x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
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
Solution
x = {3, -6}