4(a-4)+6(a+4)=1(a^2-16)

Solution for 4(a-4)+6(a+4)=1(a^2-16) equation:

Simplifying
4(a + -4) + 6(a + 4) = 1(a2 + -16)

Reorder the terms:
4(-4 + a) + 6(a + 4) = 1(a2 + -16)
(-4 * 4 + a * 4) + 6(a + 4) = 1(a2 + -16)
(-16 + 4a) + 6(a + 4) = 1(a2 + -16)

Reorder the terms:
-16 + 4a + 6(4 + a) = 1(a2 + -16)
-16 + 4a + (4 * 6 + a * 6) = 1(a2 + -16)
-16 + 4a + (24 + 6a) = 1(a2 + -16)

Reorder the terms:
-16 + 24 + 4a + 6a = 1(a2 + -16)

Combine like terms: -16 + 24 = 8
8 + 4a + 6a = 1(a2 + -16)

Combine like terms: 4a + 6a = 10a
8 + 10a = 1(a2 + -16)

Reorder the terms:
8 + 10a = 1(-16 + a2)
8 + 10a = (-16 * 1 + a2 * 1)
8 + 10a = (-16 + 1a2)

Solving
8 + 10a = -16 + 1a2

Solving for variable 'a'.

Reorder the terms:
8 + 16 + 10a + -1a2 = -16 + 1a2 + 16 + -1a2

Combine like terms: 8 + 16 = 24
24 + 10a + -1a2 = -16 + 1a2 + 16 + -1a2

Reorder the terms:
24 + 10a + -1a2 = -16 + 16 + 1a2 + -1a2

Combine like terms: -16 + 16 = 0
24 + 10a + -1a2 = 0 + 1a2 + -1a2
24 + 10a + -1a2 = 1a2 + -1a2

Combine like terms: 1a2 + -1a2 = 0
24 + 10a + -1a2 = 0

Factor a trinomial.
(12 + -1a)(2 + a) = 0

Subproblem 1
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Subproblem 2
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 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 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Solution
a = {12, -2}