(x+4)(x-19)=0

Solution for (x+4)(x-19)=0 equation:

Simplifying
(x + 4)(x + -19) = 0

Reorder the terms:
(4 + x)(x + -19) = 0

Reorder the terms:
(4 + x)(-19 + x) = 0

Multiply (4 + x) * (-19 + x)
(4(-19 + x) + x(-19 + x)) = 0
((-19 * 4 + x * 4) + x(-19 + x)) = 0
((-76 + 4x) + x(-19 + x)) = 0
(-76 + 4x + (-19 * x + x * x)) = 0
(-76 + 4x + (-19x + x2)) = 0

Combine like terms: 4x + -19x = -15x
(-76 + -15x + x2) = 0

Solving
-76 + -15x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x)(19 + -1x) = 0

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

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

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

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

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

Simplifying
x = -4
Subproblem 2
Set the factor '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 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 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {-4, 19}