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

To solve \( 8x^2 + 10x - 7 = 0 \) by factoring, we start by finding two numbers that multiply to \( 8 \times -7 = -56 \) and add to \( 10 \). These numbers are \( 14 \) and \( -4 \). Now, we rewrite the middle term: \( 8x^2 + 14x - 4x - 7 = 0 \) Next, we group the terms: \( (8x^2 + 14x) + (-4x - 7) = 0 \) Factoring gives us: \( 2x(4x + 7) - 1(4x + 7) = 0 \) Factoring out \( (4x + 7) \) results in: \( (2x - 1)(4x + 7) = 0 \) Setting each factor to zero: \( 2x - 1 = 0 \) or \( 4x + 7 = 0 \) Thus, we find the solutions: \( x = \frac{1}{2} \) or \( x = -\frac{7}{4} \) In factored form: \( (2x - 1)(4x + 7) = 0 \) The solution set is \( \{\frac{1}{2}, -\frac{7}{4}\} \).