x^2-9x+19=x-5

Solution for x^2-9x+19=x-5 equation:

Simplifying
x2 + -9x + 19 = x + -5

Reorder the terms:
19 + -9x + x2 = x + -5

Reorder the terms:
19 + -9x + x2 = -5 + x

Solving
19 + -9x + x2 = -5 + x

Solving for variable 'x'.

Reorder the terms:
19 + 5 + -9x + -1x + x2 = -5 + x + 5 + -1x

Combine like terms: 19 + 5 = 24
24 + -9x + -1x + x2 = -5 + x + 5 + -1x

Combine like terms: -9x + -1x = -10x
24 + -10x + x2 = -5 + x + 5 + -1x

Reorder the terms:
24 + -10x + x2 = -5 + 5 + x + -1x

Combine like terms: -5 + 5 = 0
24 + -10x + x2 = 0 + x + -1x
24 + -10x + x2 = x + -1x

Combine like terms: x + -1x = 0
24 + -10x + x2 = 0

Factor a trinomial.
(4 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {4, 6}