Ive the quadratic by factoring. \[ 6 x^{2}+4=-17 x+7 \]

First, let's rearrange the equation to bring all terms to one side. Adding \(17x\) and subtracting \(7\) gives us: \[ 6x^{2} + 17x + 4 - 7 = 0 \] which simplifies to: \[ 6x^{2} + 17x - 3 = 0 \] Next, we can factor this quadratic equation. We need two numbers that multiply to \(6 \times -3 = -18\) and add to \(17\). Those numbers are \(18\) and \(-1\). Thus, we can rewrite the middle term: \[ 6x^{2} + 18x - x - 3 = 0 \] Now, factor by grouping: \[ (6x^{2} + 18x) + (-x - 3) = 0 \] \[ 6x(x + 3) - 1(x + 3) = 0 \] \[ (6x - 1)(x + 3) = 0 \] Now, we set each factor equal to zero: 1. \(6x - 1 = 0 \Rightarrow x = \frac{1}{6}\) 2. \(x + 3 = 0 \Rightarrow x = -3\) So, the solutions to the equation are \(x = \frac{1}{6}\) and \(x = -3\).