Simplify \( 3(x-1)^{2}-2(x+3)(2 x-1) \)

Let's start by simplifying the given expression step by step. First, we'll expand \(3(x-1)^{2}\): \[ 3(x-1)^{2} = 3(x^{2} - 2x + 1) = 3x^{2} - 6x + 3 \] Next, we'll expand \(-2(x+3)(2x-1)\): Using the distributive property: \[ (x+3)(2x-1) = x(2x-1) + 3(2x-1) = 2x^{2} - x + 6x - 3 = 2x^{2} + 5x - 3 \] Now multiply this result by \(-2\): \[ -2(2x^{2} + 5x - 3) = -4x^{2} - 10x + 6 \] Now, combine both results: \[ 3x^{2} - 6x + 3 - 4x^{2} - 10x + 6 \] Combining like terms: Starting with \(x^{2}\) terms: \[ 3x^{2} - 4x^{2} = -x^{2} \] Now the \(x\) terms: \[ -6x - 10x = -16x \] And the constant terms: \[ 3 + 6 = 9 \] Putting it all together, we have: \[ -x^{2} - 16x + 9 \] Thus, the simplified expression is: \[ \boxed{-x^{2} - 16x + 9} \]