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=-(3)/(2) \end{gathered}`
`\begin{gathered} \: 4q+3=0 \\ q=-(3)/(4) \end{gathered}`
`\begin{gathered} 4q-3=0 \\ q=(3)/(4) \end{gathered}`

The solutions are,

`q=-(2)/(3),\: q=-(3)/(4),\: q=(3)/(4)`