67+33r=-5-3r^2

Solution for 67+33r=-5-3r^2 equation:

Simplifying
67 + 33r = -5 + -3r2

Solving
67 + 33r = -5 + -3r2

Solving for variable 'r'.

Reorder the terms:
67 + 5 + 33r + 3r2 = -5 + -3r2 + 5 + 3r2

Combine like terms: 67 + 5 = 72
72 + 33r + 3r2 = -5 + -3r2 + 5 + 3r2

Reorder the terms:
72 + 33r + 3r2 = -5 + 5 + -3r2 + 3r2

Combine like terms: -5 + 5 = 0
72 + 33r + 3r2 = 0 + -3r2 + 3r2
72 + 33r + 3r2 = -3r2 + 3r2

Combine like terms: -3r2 + 3r2 = 0
72 + 33r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 11r + r2) = 0

Factor a trinomial.
3((8 + r)(3 + 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 '(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}