(c-3)(c+2)=

Solution for (c-3)(c+2)= equation:

Simplifying
(c + -3)(c + 2) = 0

Reorder the terms:
(-3 + c)(c + 2) = 0

Reorder the terms:
(-3 + c)(2 + c) = 0

Multiply (-3 + c) * (2 + c)
(-3(2 + c) + c(2 + c)) = 0
((2 * -3 + c * -3) + c(2 + c)) = 0
((-6 + -3c) + c(2 + c)) = 0
(-6 + -3c + (2 * c + c * c)) = 0
(-6 + -3c + (2c + c2)) = 0

Combine like terms: -3c + 2c = -1c
(-6 + -1c + c2) = 0

Solving
-6 + -1c + c2 = 0

Solving for variable 'c'.

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

Subproblem 1
Set the factor '(-2 + -1c)' equal to zero and attempt to solve:

Simplifying
-2 + -1c = 0

Solving
-2 + -1c = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1c = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1c = 0 + 2
-1c = 0 + 2

Combine like terms: 0 + 2 = 2
-1c = 2

Divide each side by '-1'.
c = -2

Simplifying
c = -2
Subproblem 2
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
Solution
c = {-2, 3}