(c-5)(c+3)=0

Solution for (c-5)(c+3)=0 equation:

Simplifying
(c + -5)(c + 3) = 0

Reorder the terms:
(-5 + c)(c + 3) = 0

Reorder the terms:
(-5 + c)(3 + c) = 0

Multiply (-5 + c) * (3 + c)
(-5(3 + c) + c(3 + c)) = 0
((3 * -5 + c * -5) + c(3 + c)) = 0
((-15 + -5c) + c(3 + c)) = 0
(-15 + -5c + (3 * c + c * c)) = 0
(-15 + -5c + (3c + c2)) = 0

Combine like terms: -5c + 3c = -2c
(-15 + -2c + c2) = 0

Solving
-15 + -2c + c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-3 + -1c)(5 + -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 '(5 + -1c)' equal to zero and attempt to solve:

Simplifying
5 + -1c = 0

Solving
5 + -1c = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1c = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1c = 0 + -5
-1c = 0 + -5

Combine like terms: 0 + -5 = -5
-1c = -5

Divide each side by '-1'.
c = 5

Simplifying
c = 5
Solution
c = {-3, 5}