Part 1 of 2 Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying $x$-intercepts \[ 5 x^{2}=26 x+24 \] Rewrite the equation in factored form. \[ ]=0 \] (Factor completely.)

Step 1 ：Rewrite the equation in the standard form, which is \(ax^2 + bx + c = 0\). The given equation is \(5x^2 = 26x + 24\), so the standard form is \(5x^2 - 26x - 24 = 0\).

Step 2 ：Factor the equation. The factored form of the equation is \((x - 6)(5x + 4) = 0\).

Step 3 ：Solve for \(x\) by setting each factor equal to zero. This gives us the solutions \(x = -\frac{4}{5}\) and \(x = 6\).

Step 4 ：\(\boxed{x = -\frac{4}{5}, x = 6}\)