This equation can be simplified by using trigonometric identities.

The identity we can use is sin^2(x) + cos^2(x) = 1

Therefore, we can rewrite the equation as:

6sin^2(x) + sin(x)cos(x) - cos^2(x) = 0

Using the identity above, we can rewrite it as:

6(1 - cos^2(x)) + sin(x)cos(x) - cos^2(x) = 0

Expanding and simplifying:

6 - 6cos^2(x) + sin(x)cos(x) - cos^2(x) = 0

Rearranging terms:

6 - 7cos^2(x) + sin(x)cos(x) = 0

Therefore, the simplified form of the equation is:

7cos^2(x) - sin(x)cos(x) - 6 = 0

I hope this helps! Let me know if you have any further questions.