2c(c+1)=c^2+3

Solution for 2c(c+1)=c^2+3 equation:

Simplifying
2c(c + 1) = c2 + 3

Reorder the terms:
2c(1 + c) = c2 + 3
(1 * 2c + c * 2c) = c2 + 3
(2c + 2c2) = c2 + 3

Reorder the terms:
2c + 2c2 = 3 + c2

Solving
2c + 2c2 = 3 + c2

Solving for variable 'c'.

Reorder the terms:
-3 + 2c + 2c2 + -1c2 = 3 + c2 + -3 + -1c2

Combine like terms: 2c2 + -1c2 = 1c2
-3 + 2c + 1c2 = 3 + c2 + -3 + -1c2

Reorder the terms:
-3 + 2c + 1c2 = 3 + -3 + c2 + -1c2

Combine like terms: 3 + -3 = 0
-3 + 2c + 1c2 = 0 + c2 + -1c2
-3 + 2c + 1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
-3 + 2c + 1c2 = 0

Factor a trinomial.
(-3 + -1c)(1 + -1c) = 0

Subproblem 1
Set the factor '(-3 + -1c)' equal to zero and attempt to solve:

Simplifying
-3 + -1c = 0

Solving
-3 + -1c = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1c = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1c = 0 + 3
-1c = 0 + 3

Combine like terms: 0 + 3 = 3
-1c = 3

Divide each side by '-1'.
c = -3

Simplifying
c = -3
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 = {-3, 1}