(r+1)(r-2)=18

Solution for (r+1)(r-2)=18 equation:

Simplifying
(r + 1)(r + -2) = 18

Reorder the terms:
(1 + r)(r + -2) = 18

Reorder the terms:
(1 + r)(-2 + r) = 18

Multiply (1 + r) * (-2 + r)
(1(-2 + r) + r(-2 + r)) = 18
((-2 * 1 + r * 1) + r(-2 + r)) = 18
((-2 + 1r) + r(-2 + r)) = 18
(-2 + 1r + (-2 * r + r * r)) = 18
(-2 + 1r + (-2r + r2)) = 18

Combine like terms: 1r + -2r = -1r
(-2 + -1r + r2) = 18

Solving
-2 + -1r + r2 = 18

Solving for variable 'r'.

Reorder the terms:
-2 + -18 + -1r + r2 = 18 + -18

Combine like terms: -2 + -18 = -20
-20 + -1r + r2 = 18 + -18

Combine like terms: 18 + -18 = 0
-20 + -1r + r2 = 0

Factor a trinomial.
(-4 + -1r)(5 + -1r) = 0

Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

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

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

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-4, 5}