4r^2+11r+6=0

Solution for 4r^2+11r+6=0 equation:

Simplifying
4r2 + 11r + 6 = 0

Reorder the terms:
6 + 11r + 4r2 = 0

Solving
6 + 11r + 4r2 = 0

Solving for variable 'r'.

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

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

Simplifying
2 + r = 0

Solving
2 + r = 0

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

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

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

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

Simplifying
r = -2
Subproblem 2
Set the factor '(3 + 4r)' equal to zero and attempt to solve:

Simplifying
3 + 4r = 0

Solving
3 + 4r = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4r = 0 + -3
4r = 0 + -3

Combine like terms: 0 + -3 = -3
4r = -3

Divide each side by '4'.
r = -0.75

Simplifying
r = -0.75
Solution
r = {-2, -0.75}