A^2+(A+2)(A+2)=100

Solution for A^2+(A+2)(A+2)=100 equation:

Simplifying
A2 + (A + 2)(A + 2) = 100

Reorder the terms:
A2 + (2 + A)(A + 2) = 100

Reorder the terms:
A2 + (2 + A)(2 + A) = 100

Multiply (2 + A) * (2 + A)
A2 + (2(2 + A) + A(2 + A)) = 100
A2 + ((2 * 2 + A * 2) + A(2 + A)) = 100
A2 + ((4 + 2A) + A(2 + A)) = 100
A2 + (4 + 2A + (2 * A + A * A)) = 100
A2 + (4 + 2A + (2A + A2)) = 100

Combine like terms: 2A + 2A = 4A
A2 + (4 + 4A + A2) = 100

Reorder the terms:
4 + 4A + A2 + A2 = 100

Combine like terms: A2 + A2 = 2A2
4 + 4A + 2A2 = 100

Solving
4 + 4A + 2A2 = 100

Solving for variable 'A'.

Reorder the terms:
4 + -100 + 4A + 2A2 = 100 + -100

Combine like terms: 4 + -100 = -96
-96 + 4A + 2A2 = 100 + -100

Combine like terms: 100 + -100 = 0
-96 + 4A + 2A2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 2A + A2) = 0

Factor a trinomial.
2((-8 + -1A)(6 + -1A)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1A)' equal to zero and attempt to solve:

Simplifying
-8 + -1A = 0

Solving
-8 + -1A = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1A = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1A = 0 + 8
-1A = 0 + 8

Combine like terms: 0 + 8 = 8
-1A = 8

Divide each side by '-1'.
A = -8

Simplifying
A = -8
Subproblem 2
Set the factor '(6 + -1A)' equal to zero and attempt to solve:

Simplifying
6 + -1A = 0

Solving
6 + -1A = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1A = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1A = 0 + -6
-1A = 0 + -6

Combine like terms: 0 + -6 = -6
-1A = -6

Divide each side by '-1'.
A = 6

Simplifying
A = 6
Solution
A = {-8, 6}