a^2-20a-27=-6

Solution for a^2-20a-27=-6 equation:

Simplifying
a2 + -20a + -27 = -6

Reorder the terms:
-27 + -20a + a2 = -6

Solving
-27 + -20a + a2 = -6

Solving for variable 'a'.

Reorder the terms:
-27 + 6 + -20a + a2 = -6 + 6

Combine like terms: -27 + 6 = -21
-21 + -20a + a2 = -6 + 6

Combine like terms: -6 + 6 = 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}