Question

Solve the given equation.

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

Short answer

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

Step-by-step solution

Step 1. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign $"="$.

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^m.a^n=a^{m+n}$

Where, is any non-zero real number.

Step 3. Solve the equation, 2x(2x+3)=2(x2+3).

Use the power of a product rule to solve the equation.

$\begin{array}{c}2x\left(x+3\right)=2\left(x^2+3\right)\\ 2x\left(x\right)+2x\left(3\right)=2\left(x^2\right)+2\left(3\right)\\ 2x^2+6x=2x^2+6\\ 2x^2+6x-2x^2=6\\ 6x=6\\ x=\frac{6}{6}\\ x=1\end{array}$

Therefore, $x=1$is the solution of the given equation.