0=-24r-12-9r^2

Solution for 0=-24r-12-9r^2 equation:

Simplifying
0 = -24r + -12 + -9r2

Reorder the terms:
0 = -12 + -24r + -9r2

Solving
0 = -12 + -24r + -9r2

Solving for variable 'r'.

Combine like terms: 0 + 12 = 12
12 + 24r + 9r2 = -12 + -24r + -9r2 + 12 + 24r + 9r2

Reorder the terms:
12 + 24r + 9r2 = -12 + 12 + -24r + 24r + -9r2 + 9r2

Combine like terms: -12 + 12 = 0
12 + 24r + 9r2 = 0 + -24r + 24r + -9r2 + 9r2
12 + 24r + 9r2 = -24r + 24r + -9r2 + 9r2

Combine like terms: -24r + 24r = 0
12 + 24r + 9r2 = 0 + -9r2 + 9r2
12 + 24r + 9r2 = -9r2 + 9r2

Combine like terms: -9r2 + 9r2 = 0
12 + 24r + 9r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 8r + 3r2) = 0

Factor a trinomial.
3((2 + r)(2 + 3r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 0

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

Add '-2' to each side of the equation.
2 + -2 + r = 0 + -2

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

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

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

Simplifying
2 + 3r = 0

Solving
2 + 3r = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3r = 0 + -2
3r = 0 + -2

Combine like terms: 0 + -2 = -2
3r = -2

Divide each side by '3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Solution
r = {-2, -0.6666666667}