(x+1)(x+19)=0

Solution for (x+1)(x+19)=0 equation:

Simplifying
(x + 1)(x + 19) = 0

Reorder the terms:
(1 + x)(x + 19) = 0

Reorder the terms:
(1 + x)(19 + x) = 0

Multiply (1 + x) * (19 + x)
(1(19 + x) + x(19 + x)) = 0
((19 * 1 + x * 1) + x(19 + x)) = 0
((19 + 1x) + x(19 + x)) = 0
(19 + 1x + (19 * x + x * x)) = 0
(19 + 1x + (19x + x2)) = 0

Combine like terms: 1x + 19x = 20x
(19 + 20x + x2) = 0

Solving
19 + 20x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(19 + x)' equal to zero and attempt to solve:

Simplifying
19 + x = 0

Solving
19 + x = 0

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

Add '-19' to each side of the equation.
19 + -19 + x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + x = 0 + -19
x = 0 + -19

Combine like terms: 0 + -19 = -19
x = -19

Simplifying
x = -19
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 = {-19, -1}