6r^2+36=-33r

Solution for 6r^2+36=-33r equation:

Simplifying
6r2 + 36 = -33r

Reorder the terms:
36 + 6r2 = -33r

Solving
36 + 6r2 = -33r

Solving for variable 'r'.

Reorder the terms:
36 + 33r + 6r2 = -33r + 33r

Combine like terms: -33r + 33r = 0
36 + 33r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 11r + 2r2) = 0

Factor a trinomial.
3((4 + r)(3 + 2r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
Subproblem 2
Set the factor '(3 + 2r)' equal to zero and attempt to solve:

Simplifying
3 + 2r = 0

Solving
3 + 2r = 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 + 2r = 0 + -3

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

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

Divide each side by '2'.
r = -1.5

Simplifying
r = -1.5
Solution
r = {-4, -1.5}