To solve this equation, we need to expand the expression on the left side of the equation:

(а – 20)(а + 40) = а^2 + 40а - 20а - 800 = а^2 + 20а - 800

Now we can set this expression equal to 16,000 and solve for а:

a^2 + 20a - 800 = 16000
a^2 + 20a - 800 - 16000 = 0
a^2 + 20a - 16800 = 0

Now we can use the quadratic formula to solve for а:

a = (-b ± √(b^2 - 4ac)) / 2a

In this case, a=1, b=20, and c=-16800. Plugging these values into the formula, we get:

a = (-20 ± √(20^2 - 4(1)(-16800))) / 2(1)
a = (-20 ± √(400 + 67200)) / 2
a = (-20 ± √67600) / 2
a = (-20 ± 260) / 2

Now we can solve for both possibilities:

a = (-20 + 260) / 2 = 240 / 2 = 120
a = (-20 - 260) / 2 = -280 / 2 = -140

Therefore, the solutions for а are а = 120 or а = -140.