(c-5)(c+2)=18

Solution for (c-5)(c+2)=18 equation:

Simplifying
(c + -5)(c + 2) = 18

Reorder the terms:
(-5 + c)(c + 2) = 18

Reorder the terms:
(-5 + c)(2 + c) = 18

Multiply (-5 + c) * (2 + c)
(-5(2 + c) + c(2 + c)) = 18
((2 * -5 + c * -5) + c(2 + c)) = 18
((-10 + -5c) + c(2 + c)) = 18
(-10 + -5c + (2 * c + c * c)) = 18
(-10 + -5c + (2c + c2)) = 18

Combine like terms: -5c + 2c = -3c
(-10 + -3c + c2) = 18

Solving
-10 + -3c + c2 = 18

Solving for variable 'c'.

Reorder the terms:
-10 + -18 + -3c + c2 = 18 + -18

Combine like terms: -10 + -18 = -28
-28 + -3c + c2 = 18 + -18

Combine like terms: 18 + -18 = 0
-28 + -3c + c2 = 0

Factor a trinomial.
(-4 + -1c)(7 + -1c) = 0

Subproblem 1
Set the factor '(-4 + -1c)' equal to zero and attempt to solve:

Simplifying
-4 + -1c = 0

Solving
-4 + -1c = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1c = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1c = 0 + 4
-1c = 0 + 4

Combine like terms: 0 + 4 = 4
-1c = 4

Divide each side by '-1'.
c = -4

Simplifying
c = -4
Subproblem 2
Set the factor '(7 + -1c)' equal to zero and attempt to solve:

Simplifying
7 + -1c = 0

Solving
7 + -1c = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1c = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1c = 0 + -7
-1c = 0 + -7

Combine like terms: 0 + -7 = -7
-1c = -7

Divide each side by '-1'.
c = 7

Simplifying
c = 7
Solution
c = {-4, 7}