(a-3)(a+4)=8

Solution for (a-3)(a+4)=8 equation:

Simplifying
(a + -3)(a + 4) = 8

Reorder the terms:
(-3 + a)(a + 4) = 8

Reorder the terms:
(-3 + a)(4 + a) = 8

Multiply (-3 + a) * (4 + a)
(-3(4 + a) + a(4 + a)) = 8
((4 * -3 + a * -3) + a(4 + a)) = 8
((-12 + -3a) + a(4 + a)) = 8
(-12 + -3a + (4 * a + a * a)) = 8
(-12 + -3a + (4a + a2)) = 8

Combine like terms: -3a + 4a = 1a
(-12 + 1a + a2) = 8

Solving
-12 + 1a + a2 = 8

Solving for variable 'a'.

Reorder the terms:
-12 + -8 + 1a + a2 = 8 + -8

Combine like terms: -12 + -8 = -20
-20 + 1a + a2 = 8 + -8

Combine like terms: 8 + -8 = 0
-20 + 1a + a2 = 0

Factor a trinomial.
(-5 + -1a)(4 + -1a) = 0

Subproblem 1
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
Subproblem 2
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
Solution
a = {-5, 4}