Expanding and Simplifying the Expression
First, let's expand and simplify the left side of the equation:
(3x - 8)(3x + 2) - (4x - 11)(2x + 1)
= 9x^2 + 6x - 24x - 16 - (8x^2 + 4x - 22x - 11)
= 9x^2 + 6x - 24x - 16 - 8x^2 - 4x + 22x + 11
= x^2 - x - 5

Expanding and Simplifying the Right Side of the Equation
Now, let's expand and simplify the right side of the equation:
(x - 3)(x + 7)
= x^2 + 7x - 3x - 21
= x^2 + 4x - 21

Comparing the Left and Right Sides
Now, let's compare the simplified expressions of the left and right sides:
x^2 - x - 5 = x^2 + 4x - 21
Since the left and right sides are not equal, the given equation is not true for all values of x. The expressions on both sides are not equivalent, so the statement is false.
Therefore, the original equation (3x-8)(3x+2)-(4x-11)(2x+1)=(x-3)(x+7) is not correct for all values of x.