Question

Solve the equation. Write your answers in exact, simplified form.48q^3+32q^2-27q-18=0

Answer 1

Given an equation to solve:

$48q^3+32q^2-27q-18=0$

let us solve,

$\begin{gathered} 48q^3+32q^2-27q-18=0 \\ \mleft(3q+2\mright)\mleft(4q+3\mright)\mleft(4q-3\mright)=0 \\ 3q+2=0 \\ 4q+3=0 \\ 4q-3=0 \end{gathered}$$\begin{gathered} 3q+2=0 \\ q=-\frac{3}{2} \end{gathered}$$\begin{gathered} \: 4q+3=0 \\ q=-\frac{3}{4} \end{gathered}$$\begin{gathered} 4q-3=0 \\ q=\frac{3}{4} \end{gathered}$

The solutions are,

$q=-\frac{2}{3},\: q=-\frac{3}{4},\: q=\frac{3}{4}$