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

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

Simplifying
(C + -6)(C + 3) = 0

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

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

Multiply (-6 + C) * (3 + C)
(-6(3 + C) + C(3 + C)) = 0
((3 * -6 + C * -6) + C(3 + C)) = 0
((-18 + -6C) + C(3 + C)) = 0
(-18 + -6C + (3 * C + C * C)) = 0
(-18 + -6C + (3C + C2)) = 0

Combine like terms: -6C + 3C = -3C
(-18 + -3C + C2) = 0

Solving
-18 + -3C + C2 = 0

Solving for variable 'C'.

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

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

Simplifying
-3 + -1C = 0

Solving
-3 + -1C = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1C = 0 + 3

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

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

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

Simplifying
C = -3
Subproblem 2
Set the factor '(6 + -1C)' equal to zero and attempt to solve:

Simplifying
6 + -1C = 0

Solving
6 + -1C = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1C = 0 + -6

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

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

Divide each side by '-1'.
C = 6

Simplifying
C = 6
Solution
C = {-3, 6}