Solve by factoring \[ 3 t^{2}+4 t-20=0 \]

Step 1 ：The given equation is a quadratic equation in the form \(ax^2 + bx + c = 0\).

Step 2 ：To solve this equation by factoring, we need to express the equation in the form \((t - x)(t - y) = 0\), where \(x\) and \(y\) are the roots of the equation.

Step 3 ：The roots of the equation are -10/3 and 2. These are the values of t for which the equation equals zero.

Step 4 ：The solutions to the equation \(3 t^{2}+4 t-20=0\) are \(\boxed{-\frac{10}{3}}\) and \(\boxed{2}\).