(c-2)(c-2)=9

Solution for (c-2)(c-2)=9 equation:

Simplifying
(c + -2)(c + -2) = 9

Reorder the terms:
(-2 + c)(c + -2) = 9

Reorder the terms:
(-2 + c)(-2 + c) = 9

Multiply (-2 + c) * (-2 + c)
(-2(-2 + c) + c(-2 + c)) = 9
((-2 * -2 + c * -2) + c(-2 + c)) = 9
((4 + -2c) + c(-2 + c)) = 9
(4 + -2c + (-2 * c + c * c)) = 9
(4 + -2c + (-2c + c2)) = 9

Combine like terms: -2c + -2c = -4c
(4 + -4c + c2) = 9

Solving
4 + -4c + c2 = 9

Solving for variable 'c'.

Reorder the terms:
4 + -9 + -4c + c2 = 9 + -9

Combine like terms: 4 + -9 = -5
-5 + -4c + c2 = 9 + -9

Combine like terms: 9 + -9 = 0
-5 + -4c + c2 = 0

Factor a trinomial.
(-1 + -1c)(5 + -1c) = 0

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

Simplifying
-1 + -1c = 0

Solving
-1 + -1c = 0

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

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

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

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

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

Simplifying
c = -1
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 = {-1, 5}