5r^2+34r+45=0

Solution for 5r^2+34r+45=0 equation:

Simplifying
5r2 + 34r + 45 = 0

Reorder the terms:
45 + 34r + 5r2 = 0

Solving
45 + 34r + 5r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 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 + r = 0 + -5

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

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

Simplifying
r = -5
Subproblem 2
Set the factor '(9 + 5r)' equal to zero and attempt to solve:

Simplifying
9 + 5r = 0

Solving
9 + 5r = 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 + 5r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5r = 0 + -9
5r = 0 + -9

Combine like terms: 0 + -9 = -9
5r = -9

Divide each side by '5'.
r = -1.8

Simplifying
r = -1.8
Solution
r = {-5, -1.8}