r^2=24+2r

Solution for r^2=24+2r equation:

Simplifying
r2 = 24 + 2r

Solving
r2 = 24 + 2r

Solving for variable 'r'.

Reorder the terms:
-24 + -2r + r2 = 24 + 2r + -24 + -2r

Reorder the terms:
-24 + -2r + r2 = 24 + -24 + 2r + -2r

Combine like terms: 24 + -24 = 0
-24 + -2r + r2 = 0 + 2r + -2r
-24 + -2r + r2 = 2r + -2r

Combine like terms: 2r + -2r = 0
-24 + -2r + r2 = 0

Factor a trinomial.
(-4 + -1r)(6 + -1r) = 0

Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
Subproblem 2
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
Solution
r = {-4, 6}