a^2-2a-11=-3

Solution for a^2-2a-11=-3 equation:

Simplifying
a2 + -2a + -11 = -3

Reorder the terms:
-11 + -2a + a2 = -3

Solving
-11 + -2a + a2 = -3

Solving for variable 'a'.

Reorder the terms:
-11 + 3 + -2a + a2 = -3 + 3

Combine like terms: -11 + 3 = -8
-8 + -2a + a2 = -3 + 3

Combine like terms: -3 + 3 = 0
-8 + -2a + a2 = 0

Factor a trinomial.
(-2 + -1a)(4 + -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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-2, 4}