Solve for: ((ab)^{-1})/(cd^{-2)}

Expression: $6{x}^{2}+13x+5=0$

Write $13x$ as a sum

$6{x}^{2}+10x+3x+5=0$

Factor out $2x$ from the expression

$2x \times \left( 3x+5 \right)+3x+5=0$

Factor out $3x+5$ from the expression

$\left( 3x+5 \right) \times \left( 2x+1 \right)=0$

When the product of factors equals $0$, at least one factor is $0$

$\begin{array} { l }3x+5=0,\\2x+1=0\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=-\frac{ 5 }{ 3 },\\2x+1=0\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=-\frac{ 5 }{ 3 },\\x=-\frac{ 1 }{ 2 }\end{array}$

The equation has $2$ solutions

$\begin{align*}&\begin{array} { l }x_1=-\frac{ 5 }{ 3 },& x_2=-\frac{ 1 }{ 2 }\end{array} \\&\begin{array} { l }x_1\approx-1.66667,& x_2=-0.5\end{array}\end{align*}$