6r^2+37r+45=0

Solution for 6r^2+37r+45=0 equation:

Simplifying
6r2 + 37r + 45 = 0

Reorder the terms:
45 + 37r + 6r2 = 0

Solving
45 + 37r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(9 + 2r)(5 + 3r) = 0

Subproblem 1
Set the factor '(9 + 2r)' equal to zero and attempt to solve:

Simplifying
9 + 2r = 0

Solving
9 + 2r = 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 + 2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2r = 0 + -9
2r = 0 + -9

Combine like terms: 0 + -9 = -9
2r = -9

Divide each side by '2'.
r = -4.5

Simplifying
r = -4.5
Subproblem 2
Set the factor '(5 + 3r)' equal to zero and attempt to solve:

Simplifying
5 + 3r = 0

Solving
5 + 3r = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3r = 0 + -5
3r = 0 + -5

Combine like terms: 0 + -5 = -5
3r = -5

Divide each side by '3'.
r = -1.666666667

Simplifying
r = -1.666666667
Solution
r = {-4.5, -1.666666667}