(n-2)(n+7)=-18

Solution for (n-2)(n+7)=-18 equation:

Simplifying
(n + -2)(n + 7) = -18

Reorder the terms:
(-2 + n)(n + 7) = -18

Reorder the terms:
(-2 + n)(7 + n) = -18

Multiply (-2 + n) * (7 + n)
(-2(7 + n) + n(7 + n)) = -18
((7 * -2 + n * -2) + n(7 + n)) = -18
((-14 + -2n) + n(7 + n)) = -18
(-14 + -2n + (7 * n + n * n)) = -18
(-14 + -2n + (7n + n2)) = -18

Combine like terms: -2n + 7n = 5n
(-14 + 5n + n2) = -18

Solving
-14 + 5n + n2 = -18

Solving for variable 'n'.

Reorder the terms:
-14 + 18 + 5n + n2 = -18 + 18

Combine like terms: -14 + 18 = 4
4 + 5n + n2 = -18 + 18

Combine like terms: -18 + 18 = 0
4 + 5n + n2 = 0

Factor a trinomial.
(4 + n)(1 + n) = 0

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

Simplifying
4 + n = 0

Solving
4 + n = 0

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

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

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {-4, -1}