c^2-6c=2c+20

Solution for c^2-6c=2c+20 equation:

Simplifying
c2 + -6c = 2c + 20

Reorder the terms:
-6c + c2 = 2c + 20

Reorder the terms:
-6c + c2 = 20 + 2c

Solving
-6c + c2 = 20 + 2c

Solving for variable 'c'.

Reorder the terms:
-20 + -6c + -2c + c2 = 20 + 2c + -20 + -2c

Combine like terms: -6c + -2c = -8c
-20 + -8c + c2 = 20 + 2c + -20 + -2c

Reorder the terms:
-20 + -8c + c2 = 20 + -20 + 2c + -2c

Combine like terms: 20 + -20 = 0
-20 + -8c + c2 = 0 + 2c + -2c
-20 + -8c + c2 = 2c + -2c

Combine like terms: 2c + -2c = 0
-20 + -8c + c2 = 0

Factor a trinomial.
(-2 + -1c)(10 + -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 '(10 + -1c)' equal to zero and attempt to solve:

Simplifying
10 + -1c = 0

Solving
10 + -1c = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1c = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1c = 0 + -10
-1c = 0 + -10

Combine like terms: 0 + -10 = -10
-1c = -10

Divide each side by '-1'.
c = 10

Simplifying
c = 10
Solution
c = {-2, 10}