252=78r-6r^2

Solution for 252=78r-6r^2 equation:

Simplifying
252 = 78r + -6r2

Solving
252 = 78r + -6r2

Solving for variable 'r'.

Reorder the terms:
252 + -78r + 6r2 = 78r + -78r + -6r2 + 6r2

Combine like terms: 78r + -78r = 0
252 + -78r + 6r2 = 0 + -6r2 + 6r2
252 + -78r + 6r2 = -6r2 + 6r2

Combine like terms: -6r2 + 6r2 = 0
252 + -78r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(42 + -13r + r2) = 0

Factor a trinomial.
6((6 + -1r)(7 + -1r)) = 0

Ignore the factor 6.
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 '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {6, 7}