Let's start by distributing both terms in the equation:

(х+10)(х-5) = x^2 - 5x + 10x - 50 = x^2 + 5x - 50

(х-6)(х+3) = x^2 + 3x - 6x - 18 = x^2 - 3x - 18

Now, we can substitute these results back into the original equation:

(x^2 + 5x - 50) - (x^2 - 3x - 18) = 16

Open the parentheses:

x^2 + 5x - 50 - x^2 + 3x + 18 = 16

Simplify the equation:

8x - 32 = 16

Add 32 to both sides:

8x = 48

Divide by 8:

x = 6

Therefore, the solution to the equation is x = 6.