Quadratic Equation:
The given quadratic equation is: ad^2(ax/b - 2c/d)x bc^2 = 0

To show -bc/ad is a solution:
To show that -bc/ad is a solution of the given quadratic equation, we need to substitute -bc/ad for x in the equation and verify if it satisfies the equation.

Substituting -bc/ad for x:
Substituting -bc/ad for x in the equation, we get:
ad^2(ax/b - 2c/d)(-bc/ad)bc^2 = 0

Simplifying the equation:
Let's simplify the equation step by step:

1. Simplifying the expression inside the parentheses:
(ax/b - 2c/d) * (-bc/ad) = (-bc/ad)(ax/b) - (-bc/ad)(2c/d)
= -bc^2/(ad)(b) * ax + 2bc^2/(ad)(d) * c
= -bc^2/(ad)(b) * ax + (2bc^2c)/(ad)(d)
= -bc^2/(ad)(b) * ax + 2bc^3/(ad)(d)

2. Expanding the equation:
ad^2(-bc^2/(ad)(b) * ax + 2bc^3/(ad)(d)) * bc^2 = 0

3. Simplifying further:
- bc^2(ax) + 2bc^4/d = 0

Verifying the solution:
Now, let's substitute -bc/ad for x in the original equation and check if it holds true:

ad^2(ax/b - 2c/d) * bc^2 = 0
ad^2(-bc/ad)(ax/b - 2c/d) * bc^2 = 0
(ad^2)(-bc^2/(ad)(b) * ax + 2bc^3/(ad)(d)) * bc^2 = 0

Simplifying the equation:
- bc^2(ax) + 2bc^4/d = 0

We can observe that this equation is the same as the one we obtained earlier, which means that -bc/ad satisfies the given quadratic equation.

Therefore, we have shown that -bc/ad is a solution of the quadratic equation ad^2(ax/b - 2c/d)x bc^2 = 0.