60-7r=r^2

Solution for 60-7r=r^2 equation:

Simplifying
60 + -7r = r2

Solving
60 + -7r = r2

Solving for variable 'r'.

Combine like terms: r2 + -1r2 = 0
60 + -7r + -1r2 = 0

Factor a trinomial.
(5 + -1r)(12 + r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(12 + r)' equal to zero and attempt to solve:

Simplifying
12 + r = 0

Solving
12 + r = 0

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

Add '-12' to each side of the equation.
12 + -12 + r = 0 + -12

Combine like terms: 12 + -12 = 0
0 + r = 0 + -12
r = 0 + -12

Combine like terms: 0 + -12 = -12
r = -12

Simplifying
r = -12
Solution
r = {5, -12}