Solve the quadratic equation 5x^2 + 75x = 0

Answer 1

To solve the quadratic equation $5x^2+75x=0$, we can start by factoring the equation.

First, factor out the common term $5x$:

$$5x(x+15)=0$$

Now, set each factor equal to zero:

1. $5x=0$
2. $x+15=0$

For the first equation:

$$5x=0⟹x=0$$

For the second equation:

$$x+15=0⟹x=-15$$

Thus, the solutions to the equation $5x^2+75x=0$ are

$$\boxed{{\displaystyle 0}}\text{and}\boxed{{\displaystyle -15}}.$$