10r^2+41r+4=0

Solution for 10r^2+41r+4=0 equation:

Simplifying
10r2 + 41r + 4 = 0

Reorder the terms:
4 + 41r + 10r2 = 0

Solving
4 + 41r + 10r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(4 + r)(1 + 10r) = 0

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

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

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

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

Simplifying
r = -4
Subproblem 2
Set the factor '(1 + 10r)' equal to zero and attempt to solve:

Simplifying
1 + 10r = 0

Solving
1 + 10r = 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 + 10r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10r = 0 + -1
10r = 0 + -1

Combine like terms: 0 + -1 = -1
10r = -1

Divide each side by '10'.
r = -0.1

Simplifying
r = -0.1
Solution
r = {-4, -0.1}