24r^2+24r+6=

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

Simplifying
24r2 + 24r + 6 = 0

Reorder the terms:
6 + 24r + 24r2 = 0

Solving
6 + 24r + 24r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 4r + 4r2) = 0

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

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

Simplifying
1 + 2r = 0

Solving
1 + 2r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2r = 0 + -1

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

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

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

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

Simplifying
1 + 2r = 0

Solving
1 + 2r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2r = 0 + -1

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

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

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

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