(r+1)(7r-2)=0

Solution for (r+1)(7r-2)=0 equation:

Simplifying
(r + 1)(7r + -2) = 0

Reorder the terms:
(1 + r)(7r + -2) = 0

Reorder the terms:
(1 + r)(-2 + 7r) = 0

Multiply (1 + r) * (-2 + 7r)
(1(-2 + 7r) + r(-2 + 7r)) = 0
((-2 * 1 + 7r * 1) + r(-2 + 7r)) = 0
((-2 + 7r) + r(-2 + 7r)) = 0
(-2 + 7r + (-2 * r + 7r * r)) = 0
(-2 + 7r + (-2r + 7r2)) = 0

Combine like terms: 7r + -2r = 5r
(-2 + 5r + 7r2) = 0

Solving
-2 + 5r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -1r)(2 + -7r) = 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 '(2 + -7r)' equal to zero and attempt to solve:

Simplifying
2 + -7r = 0

Solving
2 + -7r = 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 + -7r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7r = 0 + -2
-7r = 0 + -2

Combine like terms: 0 + -2 = -2
-7r = -2

Divide each side by '-7'.
r = 0.2857142857

Simplifying
r = 0.2857142857
Solution
r = {-1, 0.2857142857}