To solve this trigonometric equation, we will manipulate the left side of the equation using trigonometric identities.

Starting with the given equation:

2sin^2(x) - cos^2(x) = sin(x)cos(x)

We know that sin^2(x) + cos^2(x) = 1 (Pythagorean identity).

Substitute sin^2(x) = 1 - cos^2(x) into the equation:

2(1 - cos^2(x)) - cos^2(x) = sin(x)cos(x)

Expanding the left side:

2 - 2cos^2(x) - cos^2(x) = sin(x)cos(x)
2 - 3cos^2(x) = sin(x)cos(x)

Rearrange the equation:

3cos^2(x) = 2 - sin(x)cos(x)

Now, we need to use the identity sin(2x) = 2sin(x)cos(x) to solve the equation.

Substitute sin(2x) into the equation:

3cos^2(x) = 2 - sin(2x)

Since sin(2x) = 2sin(x)cos(x), we get:

3cos^2(x) = 2 - 2sin(x)cos(x)

Adding 2sin(x)cos(x) to both sides:

3cos^2(x) + 2sin(x)cos(x) = 2

Hence, the equation is now in the form desired.