(c-6)(c+8)=0

Solution for (c-6)(c+8)=0 equation:

Simplifying
(c + -6)(c + 8) = 0

Reorder the terms:
(-6 + c)(c + 8) = 0

Reorder the terms:
(-6 + c)(8 + c) = 0

Multiply (-6 + c) * (8 + c)
(-6(8 + c) + c(8 + c)) = 0
((8 * -6 + c * -6) + c(8 + c)) = 0
((-48 + -6c) + c(8 + c)) = 0
(-48 + -6c + (8 * c + c * c)) = 0
(-48 + -6c + (8c + c2)) = 0

Combine like terms: -6c + 8c = 2c
(-48 + 2c + c2) = 0

Solving
-48 + 2c + c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-8 + -1c)(6 + -1c) = 0

Subproblem 1
Set the factor '(-8 + -1c)' equal to zero and attempt to solve:

Simplifying
-8 + -1c = 0

Solving
-8 + -1c = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1c = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1c = 0 + 8
-1c = 0 + 8

Combine like terms: 0 + 8 = 8
-1c = 8

Divide each side by '-1'.
c = -8

Simplifying
c = -8
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 = {-8, 6}