-3r^2-4r-1=0

Solution for -3r^2-4r-1=0 equation:

Simplifying
-3r2 + -4r + -1 = 0

Reorder the terms:
-1 + -4r + -3r2 = 0

Solving
-1 + -4r + -3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 4r + 3r2) = 0

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

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

Simplifying
1 + r = 0

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

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

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

Simplifying
r = -1
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 = {-1, -0.3333333333}