Q. 434 - Intermediate Algebra

Question

In the following exercises, solve.

$(3x-2)(x+4)=12x$

Step-by-Step Solution

Answer

Answer is $x=2,x=\frac{-4}{3}$

Step 1. Given

The equation is $(3x-2)(x+4)=12x$

Step 2. Simplify the equation

$$\begin{gathered} (3x-2)(x+4)=12x \\ 3x^2+12x-2x-8=12x \\ 3x^2-2x-8=0 \\ 3x^2-6x+4x-8=0 \\ 3x(x-2)+4(x-2)=0 \\ (x-2)(3x+4)=0 \end{gathered}$$

So,

$$\begin{gathered} x-2=0 \\ x=2 \end{gathered}$$

and

$$\begin{gathered} 3x+4=0 \\ x=\frac{-4}{3} \end{gathered}$$

Step 3. Check both the values

Put $x=2$ in original equation,

$$\begin{gathered} (3x-2)(x+4)=12x \\ (3\times 2-2)(2+4)=12\times 2 \\ 4\times 6=24 \\ 24=24 \end{gathered}$$

True

Now put $x=\frac{-4}{3}$ in the original equation,

$$\begin{gathered} (3x-2)(x+4)=12x \\ \left(3\times \frac{-4}{3}-2\right)\left(\frac{-4}{3}+4\right)=12\times \frac{-4}{3} \\ -6\left(\frac{8}{3}\right)=-16 \\ -16=-16 \end{gathered}$$

True

Step 4. Required answer

Answer is $x=2,x=\frac{-4}{3}$