Question

Solve each equation.

$\mathbf{3}\mathit{x}\left(x+2\right)\mathbf{=}\mathbf{3}\left(x^2-2\right)$

Short answer

The solution of the equation is$\mathit{x}\mathbf{=}\mathbf{-}\mathbf{1}$.

Step-by-step solution

Step 1. State the concept of multiplying a polynomial by a monomial.

To find the product of a polynomial and a monomial use the distributive property. The distributive property is given by:

$\begin{array}{l}a\left(b+c\right)=a\times b+a\times c\\ \left(a+b\right)c=a\times c+b\times c\end{array}$

Step 2. Apply the distributive property.

First, simplify both sides of the equation by applying the distributive property.

$\begin{array}{c}3x\left(x+2\right)=3\left(x^2-2\right)\\ 3x\left(x\right)+3x\left(2\right)=3\left(x^2\right)-3\left(2\right)\end{array}$

Step 3. Simplify for x.

Further, simplify the expression for x.

$\begin{array}{c}3x^2+6x=3x^2-6\\ 3x^2-3x^2+6x=-6\\ 0+6x=-6\\ x=\frac{-6}{6}\\ x=-1\end{array}$

Therefore,$x=-1$.