2c(c+2)=c^2+5

Solution for 2c(c+2)=c^2+5 equation:

Simplifying
2c(c + 2) = c2 + 5

Reorder the terms:
2c(2 + c) = c2 + 5
(2 * 2c + c * 2c) = c2 + 5
(4c + 2c2) = c2 + 5

Reorder the terms:
4c + 2c2 = 5 + c2

Solving
4c + 2c2 = 5 + c2

Solving for variable 'c'.

Reorder the terms:
-5 + 4c + 2c2 + -1c2 = 5 + c2 + -5 + -1c2

Combine like terms: 2c2 + -1c2 = 1c2
-5 + 4c + 1c2 = 5 + c2 + -5 + -1c2

Reorder the terms:
-5 + 4c + 1c2 = 5 + -5 + c2 + -1c2

Combine like terms: 5 + -5 = 0
-5 + 4c + 1c2 = 0 + c2 + -1c2
-5 + 4c + 1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
-5 + 4c + 1c2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
c = {-5, 1}