(x-19)(x-27)=0

Solution for (x-19)(x-27)=0 equation:

Simplifying
(x + -19)(x + -27) = 0

Reorder the terms:
(-19 + x)(x + -27) = 0

Reorder the terms:
(-19 + x)(-27 + x) = 0

Multiply (-19 + x) * (-27 + x)
(-19(-27 + x) + x(-27 + x)) = 0
((-27 * -19 + x * -19) + x(-27 + x)) = 0
((513 + -19x) + x(-27 + x)) = 0
(513 + -19x + (-27 * x + x * x)) = 0
(513 + -19x + (-27x + x2)) = 0

Combine like terms: -19x + -27x = -46x
(513 + -46x + x2) = 0

Solving
513 + -46x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(19 + -1x)(27 + -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 '(27 + -1x)' equal to zero and attempt to solve:

Simplifying
27 + -1x = 0

Solving
27 + -1x = 0

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

Add '-27' to each side of the equation.
27 + -27 + -1x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -1x = 0 + -27
-1x = 0 + -27

Combine like terms: 0 + -27 = -27
-1x = -27

Divide each side by '-1'.
x = 27

Simplifying
x = 27
Solution
x = {19, 27}