Solve the equation by factoring. \[ 8 x^{2}+10 x-7=0 \] The solution set is \( \{\square\} \). (Use a comma to separate answers as needed. Type each solution only once.)

To solve the equation \( 8x^2 + 10x - 7 = 0 \) by factoring, we need to express it in the form of \((ax + b)(cx + d) = 0\). First, we can look for two numbers that multiply to \( 8 \times -7 = -56 \) and add up to \( 10 \). Those numbers are \( 14 \) and \( -4 \). Rewriting the middle term, we have: \[ 8x^2 + 14x - 4x - 7 = 0. \] Next, we group the terms: \[ (8x^2 + 14x) + (-4x - 7) = 0. \] Factoring gives us: \[ 2x(4x + 7) - 1(4x + 7) = 0. \] Now factoring out the common factor: \[ (2x - 1)(4x + 7) = 0. \] Setting each factor to zero gives: 1. \( 2x - 1 = 0 \) → \( 2x = 1 \) → \( x = \frac{1}{2} \). 2. \( 4x + 7 = 0 \) → \( 4x = -7 \) → \( x = -\frac{7}{4} \). Thus, the solution set is \( \{\frac{1}{2}, -\frac{7}{4}\} \).