12*r=-27-r^2

Solution for 12*r=-27-r^2 equation:

Simplifying
12r = -27 + -1r2

Solving
12r = -27 + -1r2

Solving for variable 'r'.

Reorder the terms:
27 + 12r + r2 = -27 + -1r2 + 27 + r2

Reorder the terms:
27 + 12r + r2 = -27 + 27 + -1r2 + r2

Combine like terms: -27 + 27 = 0
27 + 12r + r2 = 0 + -1r2 + r2
27 + 12r + r2 = -1r2 + r2

Combine like terms: -1r2 + r2 = 0
27 + 12r + r2 = 0

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

Subproblem 1
Set the factor '(9 + r)' equal to zero and attempt to solve:

Simplifying
9 + r = 0

Solving
9 + r = 0

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

Add '-9' to each side of the equation.
9 + -9 + r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + r = 0 + -9
r = 0 + -9

Combine like terms: 0 + -9 = -9
r = -9

Simplifying
r = -9
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 = {-9, -3}