Solve \( 5 x^{2}+6 x-8=0 \) by factoring. Enter your answers below \( x=\square \) or \( x=\square \)

To solve the quadratic equation \( 5x^2 + 6x - 8 = 0 \) by factoring, we start by looking for two numbers that multiply to \( 5 \times -8 = -40 \) and add up to \( 6 \). The numbers \( 10 \) and \( -4 \) do the trick because \( 10 \cdot -4 = -40 \) and \( 10 + (-4) = 6 \). Next, we rewrite the middle term using these numbers: \[ 5x^2 + 10x - 4x - 8 = 0 \] Now, we group the terms: \[ (5x^2 + 10x) + (-4x - 8) = 0 \] Factoring out common factors from each group gives us: \[ 5x(x + 2) - 4(x + 2) = 0 \] Now we can factor out the common binomial: \[ (5x - 4)(x + 2) = 0 \] Setting each factor to zero gives: 1. \( 5x - 4 = 0 \) leads to \( 5x = 4 \) so \( x = \frac{4}{5} \). 2. \( x + 2 = 0 \) leads to \( x = -2 \). So, the solutions are: \( x=\frac{4}{5} \) or \( x=-2 \)