r^2-r=72

Solution for r^2-r=72 equation:

Simplifying
r2 + -1r = 72

Reorder the terms:
-1r + r2 = 72

Solving
-1r + r2 = 72

Solving for variable 'r'.

Reorder the terms:
-72 + -1r + r2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -1r + r2 = 0

Factor a trinomial.
(-8 + -1r)(9 + -1r) = 0

Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve:

Simplifying
-8 + -1r = 0

Solving
-8 + -1r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1r = 0 + 8
-1r = 0 + 8

Combine like terms: 0 + 8 = 8
-1r = 8

Divide each side by '-1'.
r = -8

Simplifying
r = -8
Subproblem 2
Set the factor '(9 + -1r)' equal to zero and attempt to solve:

Simplifying
9 + -1r = 0

Solving
9 + -1r = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1r = 0 + -9
-1r = 0 + -9

Combine like terms: 0 + -9 = -9
-1r = -9

Divide each side by '-1'.
r = 9

Simplifying
r = 9
Solution
r = {-8, 9}