(-a+3)(a+4)=0

Solution for (-a+3)(a+4)=0 equation:

Simplifying
(-1a + 3)(a + 4) = 0

Reorder the terms:
(3 + -1a)(a + 4) = 0

Reorder the terms:
(3 + -1a)(4 + a) = 0

Multiply (3 + -1a) * (4 + a)
(3(4 + a) + -1a * (4 + a)) = 0
((4 * 3 + a * 3) + -1a * (4 + a)) = 0
((12 + 3a) + -1a * (4 + a)) = 0
(12 + 3a + (4 * -1a + a * -1a)) = 0
(12 + 3a + (-4a + -1a2)) = 0

Combine like terms: 3a + -4a = -1a
(12 + -1a + -1a2) = 0

Solving
12 + -1a + -1a2 = 0

Solving for variable 'a'.

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

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
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 = {3, -4}