19.

Solve the equation using the zero-product property.

−8n(10n − 1) = 0

n = 0 or n =

n = 0 or n =

n = or n = mc003-3.jpg

n = or n = mc003-7.jpg

1 answer

To solve the equation using the zero-product property, you need to set each factor in the equation equal to zero and solve for the variable \( n \).

The given equation is:

\[ -8n(10n - 1) = 0 \]

According to the zero-product property, if the product of two factors is zero, then at least one of the factors must be zero. So we set each factor equal to zero:

1. \( -8n = 0 \)
2. \( 10n - 1 = 0 \)

Let's solve each equation separately:

1. \( -8n = 0 \)

Divide both sides by \(-8\):

\[ n = 0 \]

2. \( 10n - 1 = 0 \)

Add 1 to both sides:

\[ 10n = 1 \]

Divide both sides by 10:

\[ n = \frac{1}{10} \]

So the solutions to the equation are:

\[ n = 0 \quad \text{or} \quad n = \frac{1}{10} \]

Thus the answers are:

\[ n = 0 \quad \text{or} \quad n = \frac{1}{10} \]