r^2=60-7r

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

Simplifying
r2 = 60 + -7r

Solving
r2 = 60 + -7r

Solving for variable 'r'.

Reorder the terms:
-60 + 7r + r2 = 60 + -7r + -60 + 7r

Reorder the terms:
-60 + 7r + r2 = 60 + -60 + -7r + 7r

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

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

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

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

Simplifying
-12 + -1r = 0

Solving
-12 + -1r = 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 + -1r = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1r = 0 + 12
-1r = 0 + 12

Combine like terms: 0 + 12 = 12
-1r = 12

Divide each side by '-1'.
r = -12

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