c(c+12)=5(3+2c)

Solution for c(c+12)=5(3+2c) equation:

Simplifying
c(c + 12) = 5(3 + 2c)

Reorder the terms:
c(12 + c) = 5(3 + 2c)
(12 * c + c * c) = 5(3 + 2c)
(12c + c2) = 5(3 + 2c)
12c + c2 = (3 * 5 + 2c * 5)
12c + c2 = (15 + 10c)

Solving
12c + c2 = 15 + 10c

Solving for variable 'c'.

Reorder the terms:
-15 + 12c + -10c + c2 = 15 + 10c + -15 + -10c

Combine like terms: 12c + -10c = 2c
-15 + 2c + c2 = 15 + 10c + -15 + -10c

Reorder the terms:
-15 + 2c + c2 = 15 + -15 + 10c + -10c

Combine like terms: 15 + -15 = 0
-15 + 2c + c2 = 0 + 10c + -10c
-15 + 2c + c2 = 10c + -10c

Combine like terms: 10c + -10c = 0
-15 + 2c + c2 = 0

Factor a trinomial.
(-5 + -1c)(3 + -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 '(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
Solution
c = {-5, 3}