4r^2+5r+1=0

Solution for 4r^2+5r+1=0 equation:

Simplifying
4r2 + 5r + 1 = 0

Reorder the terms:
1 + 5r + 4r2 = 0

Solving
1 + 5r + 4r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
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 = {-1, -0.25}