Answer
\[\left\{ -\frac{5}{4},2 \right\}\]
Work Step by Step
Consider the expression\[\left( 4x+5 \right)\left( x-2 \right)=0\].
Then, by the zero product principal either \[\left( 4x+5 \right)=0\]or\[\left( x-2 \right)=0\].
Now \[\left( 4x+5 \right)=0\]implies that \[x=-\frac{5}{4}\]and \[\left( x-2 \right)=0\] implies that\[x=2\].
Next, check the proposed solution by substituting it in the original equation.
Check for\[x=-\frac{5}{4}\]. So consider,
\[\begin{align}
& \left( 4x+5 \right)\left( x-2 \right)=0 \\
& \left( 4\times \left( -\frac{5}{4} \right)+5 \right)\times \left( -\frac{5}{4}-2 \right)=0 \\
& 0\left( -\frac{5}{4}-2 \right)=0 \\
& 0=0
\end{align}\]
Now check for\[x=2\]. So consider,
\[\begin{align}
& \left( 4x+5 \right)\left( x-2 \right)=0 \\
& \left( 4\times 2+5 \right)\times \left( 2-2 \right)=0 \\
& 13\left( 0 \right)=0 \\
& 0=0
\end{align}\]
Hence, the solution set is\[\left\{ -\frac{5}{4},2 \right\}\].
