a^2-20a-19=2

Solution for a^2-20a-19=2 equation:

Simplifying
a2 + -20a + -19 = 2

Reorder the terms:
-19 + -20a + a2 = 2

Solving
-19 + -20a + a2 = 2

Solving for variable 'a'.

Reorder the terms:
-19 + -2 + -20a + a2 = 2 + -2

Combine like terms: -19 + -2 = -21
-21 + -20a + a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-21 + -20a + a2 = 0

Factor a trinomial.
(-1 + -1a)(21 + -1a) = 0

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
Subproblem 2
Set the factor '(21 + -1a)' equal to zero and attempt to solve:

Simplifying
21 + -1a = 0

Solving
21 + -1a = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1a = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1a = 0 + -21
-1a = 0 + -21

Combine like terms: 0 + -21 = -21
-1a = -21

Divide each side by '-1'.
a = 21

Simplifying
a = 21
Solution
a = {-1, 21}