r^2=-24-11r

Solution for r^2=-24-11r equation:

Simplifying
r2 = -24 + -11r

Solving
r2 = -24 + -11r

Solving for variable 'r'.

Reorder the terms:
24 + 11r + r2 = -24 + -11r + 24 + 11r

Reorder the terms:
24 + 11r + r2 = -24 + 24 + -11r + 11r

Combine like terms: -24 + 24 = 0
24 + 11r + r2 = 0 + -11r + 11r
24 + 11r + r2 = -11r + 11r

Combine like terms: -11r + 11r = 0
24 + 11r + r2 = 0

Factor a trinomial.
(8 + r)(3 + r) = 0

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

Simplifying
8 + r = 0

Solving
8 + r = 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 + r = 0 + -8

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

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

Simplifying
r = -8
Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Solution
r = {-8, -3}