5r^2+11r-16=0

Solution for 5r^2+11r-16=0 equation:

Simplifying
5r2 + 11r + -16 = 0

Reorder the terms:
-16 + 11r + 5r2 = 0

Solving
-16 + 11r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-16 + -5r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-16 + -5r)' equal to zero and attempt to solve:

Simplifying
-16 + -5r = 0

Solving
-16 + -5r = 0

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

Add '16' to each side of the equation.
-16 + 16 + -5r = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -5r = 0 + 16
-5r = 0 + 16

Combine like terms: 0 + 16 = 16
-5r = 16

Divide each side by '-5'.
r = -3.2

Simplifying
r = -3.2
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

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

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

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

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

Simplifying
r = 1
Solution
r = {-3.2, 1}