0=a^2-19a-20

Solution for 0=a^2-19a-20 equation:

Simplifying
0 = a2 + -19a + -20

Reorder the terms:
0 = -20 + -19a + a2

Solving
0 = -20 + -19a + a2

Solving for variable 'a'.

Combine like terms: 0 + 20 = 20
20 + 19a + -1a2 = -20 + -19a + a2 + 20 + 19a + -1a2

Reorder the terms:
20 + 19a + -1a2 = -20 + 20 + -19a + 19a + a2 + -1a2

Combine like terms: -20 + 20 = 0
20 + 19a + -1a2 = 0 + -19a + 19a + a2 + -1a2
20 + 19a + -1a2 = -19a + 19a + a2 + -1a2

Combine like terms: -19a + 19a = 0
20 + 19a + -1a2 = 0 + a2 + -1a2
20 + 19a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
20 + 19a + -1a2 = 0

Factor a trinomial.
(20 + -1a)(1 + a) = 0

Subproblem 1
Set the factor '(20 + -1a)' equal to zero and attempt to solve:

Simplifying
20 + -1a = 0

Solving
20 + -1a = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1a = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1a = 0 + -20
-1a = 0 + -20

Combine like terms: 0 + -20 = -20
-1a = -20

Divide each side by '-1'.
a = 20

Simplifying
a = 20
Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 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 + a = 0 + -1

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

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

Simplifying
a = -1
Solution
a = {20, -1}