5r^2+17r+6=0

Solution for 5r^2+17r+6=0 equation:

Simplifying
5r2 + 17r + 6 = 0

Reorder the terms:
6 + 17r + 5r2 = 0

Solving
6 + 17r + 5r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(2 + 5r)' equal to zero and attempt to solve:

Simplifying
2 + 5r = 0

Solving
2 + 5r = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5r = 0 + -2
5r = 0 + -2

Combine like terms: 0 + -2 = -2
5r = -2

Divide each side by '5'.
r = -0.4

Simplifying
r = -0.4
Solution
r = {-3, -0.4}