8r^2-690r+6750=0

Solution for 8r^2-690r+6750=0 equation:

Simplifying
8r2 + -690r + 6750 = 0

Reorder the terms:
6750 + -690r + 8r2 = 0

Solving
6750 + -690r + 8r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3375 + -345r + 4r2) = 0

Factor a trinomial.
2((45 + -4r)(75 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(45 + -4r)' equal to zero and attempt to solve:

Simplifying
45 + -4r = 0

Solving
45 + -4r = 0

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

Add '-45' to each side of the equation.
45 + -45 + -4r = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -4r = 0 + -45
-4r = 0 + -45

Combine like terms: 0 + -45 = -45
-4r = -45

Divide each side by '-4'.
r = 11.25

Simplifying
r = 11.25
Subproblem 2
Set the factor '(75 + -1r)' equal to zero and attempt to solve:

Simplifying
75 + -1r = 0

Solving
75 + -1r = 0

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

Add '-75' to each side of the equation.
75 + -75 + -1r = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -1r = 0 + -75
-1r = 0 + -75

Combine like terms: 0 + -75 = -75
-1r = -75

Divide each side by '-1'.
r = 75

Simplifying
r = 75
Solution
r = {11.25, 75}