5r^2+23r+26=0

Solution for 5r^2+23r+26=0 equation:

Simplifying
5r2 + 23r + 26 = 0

Reorder the terms:
26 + 23r + 5r2 = 0

Solving
26 + 23r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(13 + 5r)(2 + r) = 0

Subproblem 1
Set the factor '(13 + 5r)' equal to zero and attempt to solve:

Simplifying
13 + 5r = 0

Solving
13 + 5r = 0

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

Add '-13' to each side of the equation.
13 + -13 + 5r = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 5r = 0 + -13
5r = 0 + -13

Combine like terms: 0 + -13 = -13
5r = -13

Divide each side by '5'.
r = -2.6

Simplifying
r = -2.6
Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

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

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

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

Simplifying
r = -2
Solution
r = {-2.6, -2}