(x+6)(x+19)=0

Solution for (x+6)(x+19)=0 equation:

Simplifying
(x + 6)(x + 19) = 0

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

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

Multiply (6 + x) * (19 + x)
(6(19 + x) + x(19 + x)) = 0
((19 * 6 + x * 6) + x(19 + x)) = 0
((114 + 6x) + x(19 + x)) = 0
(114 + 6x + (19 * x + x * x)) = 0
(114 + 6x + (19x + x2)) = 0

Combine like terms: 6x + 19x = 25x
(114 + 25x + x2) = 0

Solving
114 + 25x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(19 + x)(6 + 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {-19, -6}