Q 6.93 - Intermediate Algebra

Question

Solve $(2 m+1)(m+3)=12 m$

Step-by-Step Solution

Answer

The value is $m=1,\frac{3}{2}$

Step 1: Given information

Given the equation $(2 m+1)(m+3)=12 m$

Step 2: Multiply the binomials

Multiplying the binomials, we get

$$\begin{gathered} 2m^2+6m+m+3=12m \\ 2m^2+7m+3=12m \\ 2m^2-5m+3=0 \\ 2m^2-3m-2m+3=0 \\ m(2m-3)-1(2m-3)=0 \\ (m-1)(2m-3)=0 \\ m=1,\frac{3}{2} \end{gathered}$$

Step 3: Checking the values

Substituting and checking the values, we have

$$\begin{gathered} (2\times 1+1)(1+3)=12\times 1 \\ \left(3\right)\left(4\right)=12 \\ 12=12 \\ (2\times \frac{3}{2}+1)(\frac{3}{2}+3)=12\times \frac{3}{2} \\ 4\times \frac{9}{2}=18 \\ 18=18 \end{gathered}$$

So this is correct