To solve these equations, we will simplify each equation step by step.

1) x * (-9) = 27
We can divide both sides of the equation by -9 to isolate x:
x = 27 / (-9)
x = -3

2) (-x) / 6 + 22 = (-4) * (-5)
First, let's simplify the left side of the equation:
(-x) / 6 + 22 = (-4) * (-5)
(-x) / 6 + 22 = 20
Now, let's multiply both sides of the equation by 6 to get rid of the fraction:
(-x) + 132 = 120
Next, let's subtract 132 from both sides of the equation:
-x = 120 - 132
-x = -12
Finally, let's multiply both sides of the equation by -1 to solve for x:
x = 12

3) x * (x+3) = 0
This equation is already in factored form, so we can set each factor equal to zero and solve for x:
x = 0 or x + 3 = 0
If x + 3 = 0, then x = -3.

4) (3-x) * (x+4) = 0
This equation is also in factored form, so we can set each factor equal to zero and solve for x:
3 - x = 0 or x + 4 = 0
If 3 - x = 0, then x = 3.
If x + 4 = 0, then x = -4.

So the solutions to the equations are:
x = -3, 12, 0, -3, 3, -4.