5r^2-7r-66=0

Solution for 5r^2-7r-66=0 equation:

Simplifying
5r2 + -7r + -66 = 0

Reorder the terms:
-66 + -7r + 5r2 = 0

Solving
-66 + -7r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-3 + -1r)(22 + -5r) = 0

Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

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

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(22 + -5r)' equal to zero and attempt to solve:

Simplifying
22 + -5r = 0

Solving
22 + -5r = 0

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

Add '-22' to each side of the equation.
22 + -22 + -5r = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -5r = 0 + -22
-5r = 0 + -22

Combine like terms: 0 + -22 = -22
-5r = -22

Divide each side by '-5'.
r = 4.4

Simplifying
r = 4.4
Solution
r = {-3, 4.4}