Solve by factoring. \[ \begin{array}{l}6 x^{2}-3=7 x \\ x=\square \\ \text { (Simplify your answer. Type an integer or a fraction, Use a comma to separate answers as needed.) }\end{array} \]

To solve the equation \( 6x^2 - 3 = 7x \), first, we can rearrange it into standard form: \[ 6x^2 - 7x - 3 = 0 \] Next, we will factor this quadratic equation. To do this, we need to find two numbers that multiply to \( 6 \times (-3) = -18 \) and add to \( -7 \). The numbers that fit this requirement are \( -9 \) and \( 2 \). Now we can rewrite the equation: \[ 6x^2 - 9x + 2x - 3 = 0 \] Next, we group the terms: \[ (6x^2 - 9x) + (2x - 3) = 0 \] Factoring out common factors: \[ 3x(2x - 3) + 1(2x - 3) = 0 \] Now we can factor by grouping: \[ (3x + 1)(2x - 3) = 0 \] Setting each factor to zero gives us: 1. \( 3x + 1 = 0 \) → \( 3x = -1 \) → \( x = -\frac{1}{3} \) 2. \( 2x - 3 = 0 \) → \( 2x = 3 \) → \( x = \frac{3}{2} \) Thus, the solutions are: \[ x = -\frac{1}{3}, \frac{3}{2} \]