(r+6)(-r+1)=0

Solution for (r+6)(-r+1)=0 equation:

Simplifying
(r + 6)(-1r + 1) = 0

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

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

Multiply (6 + r) * (1 + -1r)
(6(1 + -1r) + r(1 + -1r)) = 0
((1 * 6 + -1r * 6) + r(1 + -1r)) = 0
((6 + -6r) + r(1 + -1r)) = 0
(6 + -6r + (1 * r + -1r * r)) = 0
(6 + -6r + (1r + -1r2)) = 0

Combine like terms: -6r + 1r = -5r
(6 + -5r + -1r2) = 0

Solving
6 + -5r + -1r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -1r)(6 + r) = 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 '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Solution
r = {1, -6}