5r^2+11r-114=0

Solution for 5r^2+11r-114=0 equation:

Simplifying
5r2 + 11r + -114 = 0

Reorder the terms:
-114 + 11r + 5r2 = 0

Solving
-114 + 11r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -1r)(19 + -5r) = 0

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

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
Subproblem 2
Set the factor '(19 + -5r)' equal to zero and attempt to solve:

Simplifying
19 + -5r = 0

Solving
19 + -5r = 0

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

Add '-19' to each side of the equation.
19 + -19 + -5r = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -5r = 0 + -19
-5r = 0 + -19

Combine like terms: 0 + -19 = -19
-5r = -19

Divide each side by '-5'.
r = 3.8

Simplifying
r = 3.8
Solution
r = {-6, 3.8}