Step 1: Express all numbers in the equation as powers of the same base. The base 2 is suitable. $$2 = 2^1$$ $$8 = 2^3$$ $$128 = 2^7$$ Step 2: Substitute these into the given equation. $$2^{(x-3)} \times (2^3)^{(x+2)} = 2^7$$ Step 3: Apply the exponent rule $(a^m)^n = a^{mn}$ to the term $(2^3)^{(x+2)}$. $$2^{(x-3)} \times 2^{3(x+2)} = 2^7$$ $$2^{(x-3)} \times 2^{(3x+6)} = 2^7$$ Step 4: Apply the exponent rule $a^m \times a^n = a^{m+n}$ to the left side of the equation. $$2^{(x-3) + (3x+6)} = 2^7$$ $$2^{(x+3x-3+6)} = 2^7$$ $$2^{(4x+3)} = 2^7$$ Step 5: Since the bases are equal, equate the exponents. $$4x+3 = 7$$ Step 6: Solve the linear equation for $x$. $$4x = 7 - 3$$ $$4x = 4$$ $$x = \frac{4}{4}$$ $$x = 1$$ The value of $x$ is $\boxed{1}$.