a^2-5a-19=-5

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

Simplifying
a2 + -5a + -19 = -5

Reorder the terms:
-19 + -5a + a2 = -5

Solving
-19 + -5a + a2 = -5

Solving for variable 'a'.

Reorder the terms:
-19 + 5 + -5a + a2 = -5 + 5

Combine like terms: -19 + 5 = -14
-14 + -5a + a2 = -5 + 5

Combine like terms: -5 + 5 = 0
-14 + -5a + a2 = 0

Factor a trinomial.
(-2 + -1a)(7 + -1a) = 0

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

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 0

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

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

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

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

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

Simplifying
a = -2
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-2, 7}