(x+1)(x+18)=0

Solution for (x+1)(x+18)=0 equation:

Simplifying
(x + 1)(x + 18) = 0

Reorder the terms:
(1 + x)(x + 18) = 0

Reorder the terms:
(1 + x)(18 + x) = 0

Multiply (1 + x) * (18 + x)
(1(18 + x) + x(18 + x)) = 0
((18 * 1 + x * 1) + x(18 + x)) = 0
((18 + 1x) + x(18 + x)) = 0
(18 + 1x + (18 * x + x * x)) = 0
(18 + 1x + (18x + x2)) = 0

Combine like terms: 1x + 18x = 19x
(18 + 19x + x2) = 0

Solving
18 + 19x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(18 + x)(1 + x) = 0

Subproblem 1
Set the factor '(18 + x)' equal to zero and attempt to solve:

Simplifying
18 + x = 0

Solving
18 + x = 0

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

Add '-18' to each side of the equation.
18 + -18 + x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + x = 0 + -18
x = 0 + -18

Combine like terms: 0 + -18 = -18
x = -18

Simplifying
x = -18
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-18, -1}