(x-9)(x+19)=0

Solution for (x-9)(x+19)=0 equation:

Simplifying
(x + -9)(x + 19) = 0

Reorder the terms:
(-9 + x)(x + 19) = 0

Reorder the terms:
(-9 + x)(19 + x) = 0

Multiply (-9 + x) * (19 + x)
(-9(19 + x) + x(19 + x)) = 0
((19 * -9 + x * -9) + x(19 + x)) = 0
((-171 + -9x) + x(19 + x)) = 0
(-171 + -9x + (19 * x + x * x)) = 0
(-171 + -9x + (19x + x2)) = 0

Combine like terms: -9x + 19x = 10x
(-171 + 10x + x2) = 0

Solving
-171 + 10x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-19 + -1x)(9 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-19, 9}