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

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

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

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

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

Multiply (1 + r) * (-1 + 5r)
(1(-1 + 5r) + r(-1 + 5r)) = 0
((-1 * 1 + 5r * 1) + r(-1 + 5r)) = 0
((-1 + 5r) + r(-1 + 5r)) = 0
(-1 + 5r + (-1 * r + 5r * r)) = 0
(-1 + 5r + (-1r + 5r2)) = 0

Combine like terms: 5r + -1r = 4r
(-1 + 4r + 5r2) = 0

Solving
-1 + 4r + 5r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-1 + -1r = 0

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

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

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

Divide each side by '-1'.
r = -1

Simplifying
r = -1
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 = {-1, 0.2}