A^2-3A-3=7

Solution for A^2-3A-3=7 equation:

Simplifying
A2 + -3A + -3 = 7

Reorder the terms:
-3 + -3A + A2 = 7

Solving
-3 + -3A + A2 = 7

Solving for variable 'A'.

Reorder the terms:
-3 + -7 + -3A + A2 = 7 + -7

Combine like terms: -3 + -7 = -10
-10 + -3A + A2 = 7 + -7

Combine like terms: 7 + -7 = 0
-10 + -3A + A2 = 0

Factor a trinomial.
(-2 + -1A)(5 + -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 '(5 + -1A)' equal to zero and attempt to solve:

Simplifying
5 + -1A = 0

Solving
5 + -1A = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1A = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1A = 0 + -5
-1A = 0 + -5

Combine like terms: 0 + -5 = -5
-1A = -5

Divide each side by '-1'.
A = 5

Simplifying
A = 5
Solution
A = {-2, 5}