x^2-2x-19=5

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

Simplifying
x2 + -2x + -19 = 5

Reorder the terms:
-19 + -2x + x2 = 5

Solving
-19 + -2x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-19 + -5 + -2x + x2 = 5 + -5

Combine like terms: -19 + -5 = -24
-24 + -2x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-24 + -2x + 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}