(c-2)(c+3)=

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

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

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

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

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

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

Solving
-6 + 1c + c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-3 + -1c)(2 + -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 '(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
Solution
c = {-3, 2}