Factor completely. \[ -7 u^{2}-12 u+4 \]

To factor the expression \(-7 u^{2}-12 u+4\) completely, we first notice that all coefficients can be factored by -1 for simplicity. So, we rewrite it as: \[ -1(7u^2 + 12u - 4) \] Next, we look for two numbers that multiply to \(7 \cdot -4 = -28\) and add to \(12\). These two numbers are \(14\) and \(-2\). We can then rewrite the middle term: \[ -1(7u^2 + 14u - 2u - 4) \] Next, we group the terms: \[ -1\left((7u^2 + 14u) + (-2u - 4)\right) \] Factoring by grouping gives us: \[ -1\left(7u(u + 2) - 2(u + 2)\right) \] Now we can factor out the common factor \((u + 2)\): \[ -1(7u - 2)(u + 2) \] Thus, the completely factored form of the expression is: \[ -1(7u - 2)(u + 2) \] Or simply: \[ -(7u - 2)(u + 2) \]