To solve the equation \( 2x^2 + 6x - 60 = 20 \) by factoring, we first need to set the equation to zero:
\[ 2x^2 + 6x - 60 - 20 = 0 \] \[ 2x^2 + 6x - 80 = 0 \]
Next, we can simplify the equation by dividing every term by 2:
\[ x^2 + 3x - 40 = 0 \]
Now, we can factor the quadratic. We are looking for two numbers that multiply to \(-40\) (the constant term) and add to \(3\) (the coefficient of the linear term).
The numbers that satisfy this condition are \(8\) and \(-5\). Thus, we can factor the equation as follows:
\[ (x + 8)(x - 5) = 0 \]
Using the zero product property, we set each factor equal to zero:
- \(x + 8 = 0 \implies x = -8\)
- \(x - 5 = 0 \implies x = 5\)
Thus, the solutions to the equation are:
\[ x = 5, -8 \]
So the correct answer is:
x = 5, -8.