Question 9 (1 point) Solve the equation using the zero-product property. \[ -8 n(10 n-1)=0 \] a \( n=-\frac{1}{8} \) or \( n=-\frac{1}{10} \) b \( n=0 \) or \( n=\frac{1}{10} \) c \( n=0 \) or \( n=-\frac{1}{10} \) d \( n=-\frac{1}{8} \) or \( n=\frac{1}{10} \) Question 10 (1 point) Solve the equation by factoring. \[ 3 z^{2}+3 z-6=0 \] a \( \quad z=3 \) or \( z=-2 \) b \( z=1 \) or \( z=-2 \) c \( z=1 \) or \( z=2 \) d \( z=3 \) or \( z=2 \)

Solve the equation \( -8n(10n-1)=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(-8n\left(10n-1\right)=0\) - step1: Divide the terms: \(n\left(10n-1\right)=0\) - step2: Separate into possible cases: \(\begin{align}&10n-1=0\\&n=0\end{align}\) - step3: Solve the equation: \(\begin{align}&n=\frac{1}{10}\\&n=0\end{align}\) - step4: Rewrite: \(n_{1}=0,n_{2}=\frac{1}{10}\) The solutions to the equation \(-8n(10n-1)=0\) are \(n=0\) or \(n=\frac{1}{10}\). Now, let's solve the equation \(3z^{2}+3z-6=0\) by factoring. Solve the quadratic equation by following steps: - step0: Solve by factoring: \(3z^{2}+3z-6=0\) - step1: Factor the expression: \(3\left(z-1\right)\left(z+2\right)=0\) - step2: Divide the terms: \(\left(z-1\right)\left(z+2\right)=0\) - step3: Separate into possible cases: \(\begin{align}&z-1=0\\&z+2=0\end{align}\) - step4: Solve the equation: \(\begin{align}&z=1\\&z=-2\end{align}\) - step5: Rewrite: \(z_{1}=-2,z_{2}=1\) The solutions to the equation \(3z^{2}+3z-6=0\) are \(z=-2\) or \(z=1\). Therefore, the correct answers are: - Question 9: b \( n=0 \) or \( n=\frac{1}{10} \) - Question 10: a \( z=-2 \) or \( z=1 \)