36r^2+24r+4=0

Solution for 36r^2+24r+4=0 equation:

Simplifying
36r2 + 24r + 4 = 0

Reorder the terms:
4 + 24r + 36r2 = 0

Solving
4 + 24r + 36r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 6r + 9r2) = 0

Factor a trinomial.
4((1 + 3r)(1 + 3r)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 3r)' equal to zero and attempt to solve:

Simplifying
1 + 3r = 0

Solving
1 + 3r = 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 + 3r = 0 + -1

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

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

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Subproblem 2
Set the factor '(1 + 3r)' equal to zero and attempt to solve:

Simplifying
1 + 3r = 0

Solving
1 + 3r = 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 + 3r = 0 + -1

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

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

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Solution
r = {-0.3333333333, -0.3333333333}