Use the​ zero-product property to solve the following equation.negative 5 n left parenthesis 5 n minus 6 right parenthesisequals0Question content area bottomPart 1n​ =enter your response here ​(Simplify your answer. Use a comma to separate answers as​ needed.)

Answer 1

To solve the equation \(-5n(5n - 6) = 0\) using the zero-product property, we can set each factor equal to zero.

The equation can be broken down into two factors:

1. \(-5n = 0\)
2. \(5n - 6 = 0\)

Now we solve each factor separately.

1. For \(-5n = 0\): \[ n = 0 \]

2. For \(5n - 6 = 0\): \[ 5n = 6 \] \[ n = \frac{6}{5} \]

So the solutions to the equation are: \[ n = 0, \frac{6}{5} \]

Thus, the final answer is: \[ n = 0, \frac{6}{5} \]