24c^2+24c+6=

Solution for 24c^2+24c+6= equation:

Simplifying
24c2 + 24c + 6 = 0

Reorder the terms:
6 + 24c + 24c2 = 0

Solving
6 + 24c + 24c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 4c + 4c2) = 0

Factor a trinomial.
6((1 + 2c)(1 + 2c)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + 2c)' equal to zero and attempt to solve:

Simplifying
1 + 2c = 0

Solving
1 + 2c = 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 + 2c = 0 + -1

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

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

Divide each side by '2'.
c = -0.5

Simplifying
c = -0.5
Subproblem 2
Set the factor '(1 + 2c)' equal to zero and attempt to solve:

Simplifying
1 + 2c = 0

Solving
1 + 2c = 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 + 2c = 0 + -1

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

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

Divide each side by '2'.
c = -0.5

Simplifying
c = -0.5
Solution
c = {-0.5, -0.5}