21r^2+62r+45=0

Solution for 21r^2+62r+45=0 equation:

Simplifying
21r2 + 62r + 45 = 0

Reorder the terms:
45 + 62r + 21r2 = 0

Solving
45 + 62r + 21r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + 3r)(9 + 7r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + 7r)' equal to zero and attempt to solve:

Simplifying
9 + 7r = 0

Solving
9 + 7r = 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 + 7r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 7r = 0 + -9
7r = 0 + -9

Combine like terms: 0 + -9 = -9
7r = -9

Divide each side by '7'.
r = -1.285714286

Simplifying
r = -1.285714286
Solution
r = {-1.666666667, -1.285714286}