To solve this equation, we need to first simplify both sides of the equation.

Starting with the left side:
-7x^2 + 13x + 9

Now, let's simplify the right side:
-19 + 13x
Rearranging this gives us:
13x - 19

Now our equation looks like this:
-7x^2 + 13x + 9 = 13x - 19

Next, we will move all terms to one side of the equation to set it equal to zero:
-7x^2 + 13x + 9 - 13x + 19 = 0
-7x^2 + 9 + 19 = 0
-7x^2 + 28 = 0

Now, we can solve for x by factoring:
-7(x^2 - 4) = 0
-7(x + 2)(x - 2) = 0

Setting each factor equal to zero:
x + 2 = 0
x = -2

and

x - 2 = 0
x = 2

Therefore, the solution to the equation is x = -2 or x = 2.