240=22r+r^2

Solution for 240=22r+r^2 equation:

Simplifying
240 = 22r + r2

Solving
240 = 22r + r2

Solving for variable 'r'.

Reorder the terms:
240 + -22r + -1r2 = 22r + -22r + r2 + -1r2

Combine like terms: 22r + -22r = 0
240 + -22r + -1r2 = 0 + r2 + -1r2
240 + -22r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
240 + -22r + -1r2 = 0

Factor a trinomial.
(8 + -1r)(30 + r) = 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 '(30 + r)' equal to zero and attempt to solve:

Simplifying
30 + r = 0

Solving
30 + r = 0

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

Add '-30' to each side of the equation.
30 + -30 + r = 0 + -30

Combine like terms: 30 + -30 = 0
0 + r = 0 + -30
r = 0 + -30

Combine like terms: 0 + -30 = -30
r = -30

Simplifying
r = -30
Solution
r = {8, -30}