12r^2+38r+16=0

Solution for 12r^2+38r+16=0 equation:

Simplifying
12r2 + 38r + 16 = 0

Reorder the terms:
16 + 38r + 12r2 = 0

Solving
16 + 38r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 19r + 6r2) = 0

Factor a trinomial.
2((8 + 3r)(1 + 2r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + 3r)' equal to zero and attempt to solve:

Simplifying
8 + 3r = 0

Solving
8 + 3r = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3r = 0 + -8
3r = 0 + -8

Combine like terms: 0 + -8 = -8
3r = -8

Divide each side by '3'.
r = -2.666666667

Simplifying
r = -2.666666667
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 = {-2.666666667, -0.5}