I'm trying to solve a quadratic by factoring, the equation given is $3{x}^{2} + 5x = 6$
The first thing I did to try and solve it is by putting the $6$ on to the other side of the equation making it $3{x}^{2} + 5x - 6$ Though, trying to solve it now by looking at some common factor and, it looks like it's not even possible to factor properly. Any help with this?
For any quadratic equation $cx^2+a_1x+b_1=0$ with $c \neq 0$ ($c = 0$ leads to a linear equation) we can divide both sides by $c$ to get $$x^2+ax+b=0$$
In general for any equation $x^2+ax+b=0$: $0=x^2+ax+b=x^2+ax+(\frac{a}{2})^2-(\frac{a}{2})^2 +b= (x+\frac{a}{2})^2-(\frac{a}{2})^2 +b$ so we obtain
$$(x+\frac{a}{2})^2-((\frac{a}{2})^2-b)=0$$
Now factor as a difference of squares if possible