(a+4)2-(a-4)(a+4)=

Solution for (a+4)2-(a-4)(a+4)= equation:

Simplifying
(a + 4) * 2 + -1(a + -4)(a + 4) = 0

Reorder the terms:
(4 + a) * 2 + -1(a + -4)(a + 4) = 0

Reorder the terms for easier multiplication:
2(4 + a) + -1(a + -4)(a + 4) = 0
(4 * 2 + a * 2) + -1(a + -4)(a + 4) = 0
(8 + 2a) + -1(a + -4)(a + 4) = 0

Reorder the terms:
8 + 2a + -1(-4 + a)(a + 4) = 0

Reorder the terms:
8 + 2a + -1(-4 + a)(4 + a) = 0

Multiply (-4 + a) * (4 + a)
8 + 2a + -1(-4(4 + a) + a(4 + a)) = 0
8 + 2a + -1((4 * -4 + a * -4) + a(4 + a)) = 0
8 + 2a + -1((-16 + -4a) + a(4 + a)) = 0
8 + 2a + -1(-16 + -4a + (4 * a + a * a)) = 0
8 + 2a + -1(-16 + -4a + (4a + a2)) = 0

Combine like terms: -4a + 4a = 0
8 + 2a + -1(-16 + 0 + a2) = 0
8 + 2a + -1(-16 + a2) = 0
8 + 2a + (-16 * -1 + a2 * -1) = 0
8 + 2a + (16 + -1a2) = 0

Reorder the terms:
8 + 16 + 2a + -1a2 = 0

Combine like terms: 8 + 16 = 24
24 + 2a + -1a2 = 0

Solving
24 + 2a + -1a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6 + -1a)(4 + a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 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 + a = 0 + -4

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

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

Simplifying
a = -4
Solution
a = {6, -4}