c^2=4(1+c+2)

Solution for c^2=4(1+c+2) equation:

Simplifying
c2 = 4(1 + c + 2)

Reorder the terms:
c2 = 4(1 + 2 + c)

Combine like terms: 1 + 2 = 3
c2 = 4(3 + c)
c2 = (3 * 4 + c * 4)
c2 = (12 + 4c)

Solving
c2 = 12 + 4c

Solving for variable 'c'.

Reorder the terms:
-12 + -4c + c2 = 12 + 4c + -12 + -4c

Reorder the terms:
-12 + -4c + c2 = 12 + -12 + 4c + -4c

Combine like terms: 12 + -12 = 0
-12 + -4c + c2 = 0 + 4c + -4c
-12 + -4c + c2 = 4c + -4c

Combine like terms: 4c + -4c = 0
-12 + -4c + c2 = 0

Factor a trinomial.
(-2 + -1c)(6 + -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 '(6 + -1c)' equal to zero and attempt to solve:

Simplifying
6 + -1c = 0

Solving
6 + -1c = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1c = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1c = 0 + -6
-1c = 0 + -6

Combine like terms: 0 + -6 = -6
-1c = -6

Divide each side by '-1'.
c = 6

Simplifying
c = 6
Solution
c = {-2, 6}