To simplify this expression, we can rewrite it in terms of sine and cosine using the identity sin^2(x) + cos^2(x) = 1.

We have: 7sin^2(x) - 5sin(x)cos(x) - cos^2(x) = 0

Replacing sin^2(x) with 1 - cos^2(x), we get:

7(1 - cos^2(x)) - 5sin(x)cos(x) - cos^2(x) = 0

Expanding, we get:

7 - 7cos^2(x) - 5sin(x)cos(x) - cos^2(x) = 0

Rewriting this expression in terms of sin(2x) using the identity sin(2x) = 2sin(x)cos(x), we get:

7 - 7cos^2(x) - 5sin(2x) - cos^2(x) = 0

Combining like terms, we get:

-8cos^2(x) - 5sin(2x) + 7 = 0

Therefore, the simplified expression is: -8cos^2(x) - 5sin(2x) + 7 = 0.