3r^2+27r=-24

Solution for 3r^2+27r=-24 equation:

Simplifying
3r2 + 27r = -24

Reorder the terms:
27r + 3r2 = -24

Solving
27r + 3r2 = -24

Solving for variable 'r'.

Reorder the terms:
24 + 27r + 3r2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 27r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 9r + r2) = 0

Factor a trinomial.
3((8 + r)(1 + r)) = 0

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

Simplifying
1 + r = 0

Solving
1 + r = 0

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

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

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

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

Simplifying
r = -1
Solution
r = {-8, -1}