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

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

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

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

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

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

Combine like terms: -9x + -19x = -28x
0 = (171 + -28x + x2)

Solving
0 = 171 + -28x + x2

Solving for variable 'x'.

Combine like terms: 0 + -171 = -171
-171 + 28x + -1x2 = 171 + -28x + x2 + -171 + 28x + -1x2

Reorder the terms:
-171 + 28x + -1x2 = 171 + -171 + -28x + 28x + x2 + -1x2

Combine like terms: 171 + -171 = 0
-171 + 28x + -1x2 = 0 + -28x + 28x + x2 + -1x2
-171 + 28x + -1x2 = -28x + 28x + x2 + -1x2

Combine like terms: -28x + 28x = 0
-171 + 28x + -1x2 = 0 + x2 + -1x2
-171 + 28x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-171 + 28x + -1x2 = 0

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