Question

Solve the equation. $$ 8(9 n+27)(6 n-9)=0 $$

Short answer

The solutions to the equation \(8(9n+27)(6n-9)=0\) are \(n=-3\) and \(n=1.5\).

Step-by-step solution

Identify the terms

The first step is to identify the terms of the equation. In the equation \(8(9n+27)(6n-9)=0\), there are three terms, namely \(8\), \((9n+27)\) and \((6n-9)\).

Set each term to zero and solve

The next step is to set each term equal to zero and solve. Solving for \(8\) being zero won’t provide any solution since \(8\) is a constant and cannot be zero. Solving for \(9n+27=0\), we get \(n=-3\). Solving for \(6n-9=0\), we get \(n=1.5\).

Presenting the solutions

Now that each possible value of \(n\) is found that satisfy equation \(8(9n+27)(6n-9)=0\), it’s time to present the solutions in the proper mathematical notation. The solutions are \(n=-3\) and \(n=1.5\).