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

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

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

Reorder the terms:
a + 4 + -1a(4 + a) = 0
a + 4 + (4 * -1a + a * -1a) = 0
a + 4 + (-4a + -1a2) = 0

Reorder the terms:
4 + a + -4a + -1a2 = 0

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

Solving
4 + -3a + -1a2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
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 = {1, -4}