To solve this equation, we will first eliminate the logarithm by raising both sides of the equation as a power of 10. This will allow us to cancel out the logarithm function.

So we have:

2x^2 + 3x = 6x + 2

Now let's simplify this equation by moving all terms to one side:

2x^2 + 3x - 6x - 2 = 0

Rearranging the terms:

2x^2 - 3x - 2 = 0

Now we have a quadratic equation. Let's solve it by factoring or using the quadratic formula:

We can factor this equation as:

(2x + 1)(x - 2) = 0

This gives us two possible solutions:

2x + 1 = 0
x = -1/2

x - 2 = 0
x = 2

So the two solutions for the given equation are x = -1/2 and x = 2.