To solve the first equation, we need to find two numbers that multiply to -32 and add up to -14. These numbers are -16 and 2. Therefore, we can rewrite the equation as:

[ (x - 16)(x + 2) = 0 ]

Setting each factor to zero gives us:

[ x - 16 = 0 \Rightarrow x = 16 ]

[ x + 2 = 0 \Rightarrow x = -2 ]

So, the solutions to the first equation are ( x = 16 ) and ( x = -2 ).

To solve the second equation by factoring, we need to find two numbers that multiply to -30 and add up to 1. These numbers are -5 and 6. Therefore, we can rewrite the equation as:

[ (-2x - 5)(x - 3) = 0 ]

Setting each factor to zero gives us:

[ -2x - 5 = 0 \Rightarrow x = -\frac{5}{2} ]

[ x - 3 = 0 \Rightarrow x = 3 ]

Therefore, the solutions to the second equation are ( x = -\frac{5}{2} ) and ( x = 3 ).