(r+1)(r-3)=

Solution for (r+1)(r-3)= equation:

Simplifying
(r + 1)(r + -3) = 0

Reorder the terms:
(1 + r)(r + -3) = 0

Reorder the terms:
(1 + r)(-3 + r) = 0

Multiply (1 + r) * (-3 + r)
(1(-3 + r) + r(-3 + r)) = 0
((-3 * 1 + r * 1) + r(-3 + r)) = 0
((-3 + 1r) + r(-3 + r)) = 0
(-3 + 1r + (-3 * r + r * r)) = 0
(-3 + 1r + (-3r + r2)) = 0

Combine like terms: 1r + -3r = -2r
(-3 + -2r + r2) = 0

Solving
-3 + -2r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -1r)(3 + -1r) = 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 '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-1, 3}