Question

Solve each equation. Check your solution.

$\mathbf{6}{p}^2-\mathbf{3}p=\mathbf{0}$

Short answer

The solution of$6p^2-3p=0$ is $p=\mathbf{0}\mathbf{,}\frac{1}{2}$.

Step-by-step solution

Step 1. Factor by using GCF.

Factor by using GCF to get the form $xy=0$.

$3p\left(2p-1\right)=0$

Step 2. Write zero product property.

For any real numbers x and y, if$xy=0$ then$x=0,y=0$ or both x and y equal to zero.

Step 3. Apply zero product property.

Apply zero product property to the given equation, $3p\left(2p-1\right)=0$.

$$\begin{gathered} 3p=0\text{or}2p-1=0 \\ p=0\text{p}=\frac{1}{2} \end{gathered}$$

Therefore, the roots are 0 and $\frac{1}{2}$.

Step 4. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute 0 for p and$\frac{1}{2}$ for p in the given equation and simplify.

$$\begin{gathered} 6{\left(0\right)}^2\stackrel{?}{=}0 \\ 0=0✓ \end{gathered}$$

$$\begin{gathered} 6{\left(\frac{1}{2}\right)}^2-3\left(\frac{1}{2}\right)\stackrel{?}{=}0 \\ 0=0✓ \end{gathered}$$

Therefore, the obtained solution is correct.