(r+2)(5r+1)=0

Solution for (r+2)(5r+1)=0 equation:

Simplifying
(r + 2)(5r + 1) = 0

Reorder the terms:
(2 + r)(5r + 1) = 0

Reorder the terms:
(2 + r)(1 + 5r) = 0

Multiply (2 + r) * (1 + 5r)
(2(1 + 5r) + r(1 + 5r)) = 0
((1 * 2 + 5r * 2) + r(1 + 5r)) = 0
((2 + 10r) + r(1 + 5r)) = 0
(2 + 10r + (1 * r + 5r * r)) = 0
(2 + 10r + (1r + 5r2)) = 0

Combine like terms: 10r + 1r = 11r
(2 + 11r + 5r2) = 0

Solving
2 + 11r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + r)(1 + 5r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 5r)' equal to zero and attempt to solve:

Simplifying
1 + 5r = 0

Solving
1 + 5r = 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 + 5r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5r = 0 + -1
5r = 0 + -1

Combine like terms: 0 + -1 = -1
5r = -1

Divide each side by '5'.
r = -0.2

Simplifying
r = -0.2
Solution
r = {-2, -0.2}