Final answer:
The real solutions of the equation -5x² -6x=0 are found by factoring out a common factor, resulting in x equals 0 and x equals -1.2.
Step-by-step explanation:
The equation provided, -5x² -6x=0, can be solved by factoring or using the quadratic formula. However, since this is a relatively simple quadratic equation, we can solve it by factoring. We start by identifying the common factor in both terms, which is -x.
First, factor out -x from the equation: -x(5x + 6) = 0. Then, we set each factor equal to zero and solve for x. This gives us two solutions: x=0 and x=-6/5 or x=-1.2. These are the real solutions of the equation.