16r^2=60+68r

Solution for 16r^2=60+68r equation:

Simplifying
16r2 = 60 + 68r

Solving
16r2 = 60 + 68r

Solving for variable 'r'.

Reorder the terms:
-60 + -68r + 16r2 = 60 + 68r + -60 + -68r

Reorder the terms:
-60 + -68r + 16r2 = 60 + -60 + 68r + -68r

Combine like terms: 60 + -60 = 0
-60 + -68r + 16r2 = 0 + 68r + -68r
-60 + -68r + 16r2 = 68r + -68r

Combine like terms: 68r + -68r = 0
-60 + -68r + 16r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -17r + 4r2) = 0

Factor a trinomial.
4((-3 + -4r)(5 + -1r)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-0.75, 5}