4r^2+13r+9=0

Solution for 4r^2+13r+9=0 equation:

Simplifying
4r2 + 13r + 9 = 0

Reorder the terms:
9 + 13r + 4r2 = 0

Solving
9 + 13r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(9 + 4r)(1 + r) = 0

Subproblem 1
Set the factor '(9 + 4r)' equal to zero and attempt to solve:

Simplifying
9 + 4r = 0

Solving
9 + 4r = 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 + 4r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4r = 0 + -9
4r = 0 + -9

Combine like terms: 0 + -9 = -9
4r = -9

Divide each side by '4'.
r = -2.25

Simplifying
r = -2.25
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 0

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

Add '-1' to each side of the equation.
1 + -1 + r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + r = 0 + -1
r = 0 + -1

Combine like terms: 0 + -1 = -1
r = -1

Simplifying
r = -1
Solution
r = {-2.25, -1}