x^2-10x-19=5

Solution for x^2-10x-19=5 equation:

Simplifying
x2 + -10x + -19 = 5

Reorder the terms:
-19 + -10x + x2 = 5

Solving
-19 + -10x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-19 + -5 + -10x + x2 = 5 + -5

Combine like terms: -19 + -5 = -24
-24 + -10x + x2 = 5 + -5

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

Factor a trinomial.
(-2 + -1x)(12 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-2, 12}