(a+3)(8)-(a-5)=(a-1)(a+1)+(a+3)(6)

Solution for (a+3)(8)-(a-5)=(a-1)(a+1)+(a+3)(6) equation:

Simplifying
(a + 3)(8) + -1(a + -5) = (a + -1)(a + 1) + (a + 3)(6)

Reorder the terms:
(3 + a)(8) + -1(a + -5) = (a + -1)(a + 1) + (a + 3)(6)

Reorder the terms for easier multiplication:
8(3 + a) + -1(a + -5) = (a + -1)(a + 1) + (a + 3)(6)
(3 * 8 + a * 8) + -1(a + -5) = (a + -1)(a + 1) + (a + 3)(6)
(24 + 8a) + -1(a + -5) = (a + -1)(a + 1) + (a + 3)(6)

Reorder the terms:
24 + 8a + -1(-5 + a) = (a + -1)(a + 1) + (a + 3)(6)
24 + 8a + (-5 * -1 + a * -1) = (a + -1)(a + 1) + (a + 3)(6)
24 + 8a + (5 + -1a) = (a + -1)(a + 1) + (a + 3)(6)

Reorder the terms:
24 + 5 + 8a + -1a = (a + -1)(a + 1) + (a + 3)(6)

Combine like terms: 24 + 5 = 29
29 + 8a + -1a = (a + -1)(a + 1) + (a + 3)(6)

Combine like terms: 8a + -1a = 7a
29 + 7a = (a + -1)(a + 1) + (a + 3)(6)

Reorder the terms:
29 + 7a = (-1 + a)(a + 1) + (a + 3)(6)

Reorder the terms:
29 + 7a = (-1 + a)(1 + a) + (a + 3)(6)

Multiply (-1 + a) * (1 + a)
29 + 7a = (-1(1 + a) + a(1 + a)) + (a + 3)(6)
29 + 7a = ((1 * -1 + a * -1) + a(1 + a)) + (a + 3)(6)
29 + 7a = ((-1 + -1a) + a(1 + a)) + (a + 3)(6)
29 + 7a = (-1 + -1a + (1 * a + a * a)) + (a + 3)(6)
29 + 7a = (-1 + -1a + (1a + a2)) + (a + 3)(6)

Combine like terms: -1a + 1a = 0
29 + 7a = (-1 + 0 + a2) + (a + 3)(6)
29 + 7a = (-1 + a2) + (a + 3)(6)

Reorder the terms:
29 + 7a = -1 + a2 + (3 + a)(6)

Reorder the terms for easier multiplication:
29 + 7a = -1 + a2 + 6(3 + a)
29 + 7a = -1 + a2 + (3 * 6 + a * 6)
29 + 7a = -1 + a2 + (18 + 6a)

Reorder the terms:
29 + 7a = -1 + 18 + 6a + a2

Combine like terms: -1 + 18 = 17
29 + 7a = 17 + 6a + a2

Solving
29 + 7a = 17 + 6a + a2

Solving for variable 'a'.

Reorder the terms:
29 + -17 + 7a + -6a + -1a2 = 17 + 6a + a2 + -17 + -6a + -1a2

Combine like terms: 29 + -17 = 12
12 + 7a + -6a + -1a2 = 17 + 6a + a2 + -17 + -6a + -1a2

Combine like terms: 7a + -6a = 1a
12 + 1a + -1a2 = 17 + 6a + a2 + -17 + -6a + -1a2

Reorder the terms:
12 + 1a + -1a2 = 17 + -17 + 6a + -6a + a2 + -1a2

Combine like terms: 17 + -17 = 0
12 + 1a + -1a2 = 0 + 6a + -6a + a2 + -1a2
12 + 1a + -1a2 = 6a + -6a + a2 + -1a2

Combine like terms: 6a + -6a = 0
12 + 1a + -1a2 = 0 + a2 + -1a2
12 + 1a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
12 + 1a + -1a2 = 0

Factor a trinomial.
(4 + -1a)(3 + a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Solution
a = {4, -3}