4r^2+13r+3=0

Solution for 4r^2+13r+3=0 equation:

Simplifying
4r2 + 13r + 3 = 0

Reorder the terms:
3 + 13r + 4r2 = 0

Solving
3 + 13r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + r)(1 + 4r) = 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 '(1 + 4r)' equal to zero and attempt to solve:

Simplifying
1 + 4r = 0

Solving
1 + 4r = 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 + 4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4r = 0 + -1
4r = 0 + -1

Combine like terms: 0 + -1 = -1
4r = -1

Divide each side by '4'.
r = -0.25

Simplifying
r = -0.25
Solution
r = {-3, -0.25}