Q. 6.87 - Intermediate Algebra

Question

Solve, $(3 m-2)(2 m+1)=0$

Step-by-Step Solution

Answer

The value is $m=\frac{2}{3},\frac{-1}{2}$

Step 1: Given information

Given the equation $(3 m-2)(2 m+1)=0$

Step 2: Using the zero factor principle

Using the principle, we get

$$\begin{gathered} (3 m-2)(2 m+1)=0 \\ 3m-2=0 \\ 2m+1=0 \\ m=\frac{2}{3},\frac{-1}{2} \end{gathered}$$

Step 3: Checking the values

Substituting the values and checking, we get

$$\begin{gathered} (3 m-2)(2 m+1)=0 \\ (3\times \frac{2}{3}-2)(2\times \frac{2}{3}+1)=0 \\ 0=0 \end{gathered}$$

This is true

Step 4: Checking another value

Checking the other value, we get

$$\begin{gathered} (3 m-2)(2 m+1)=0 \\ (3\times \frac{-1}{2})(2\times \frac{-1}{2}+1)=0 \\ 0=0 \end{gathered}$$

This is true