Rewrite the expression by factoring out $(x-4)$. \[ 3 x^{2}(x-4)-7(x-4) \]

Step 1 ：Rewrite the expression by factoring out \((x-4)\). The expression given is \(3 x^{2}(x-4)-7(x-4)\). Both terms in the expression have a common factor of \((x-4)\). Factoring out means to rewrite the expression such that \((x-4)\) is taken out common. This is a simple algebraic manipulation and does not require any calculations.

Step 2 ：The expression factored out by \((x-4)\) is \((x-4)(3x^2-7)\).