Solving Equations by Factorising

We can factorise by finding a pair of factors which multiply to make $12$, and add together to give $-7$.

This means that we have two solutions for $x$, one in each bracket. So, we effectively have $x-3=0$ and $x-4=0$

$x\space\cancel{-3}=0+3$ so $x=3$

Therefore, there are two solutions to the equation. $x=3$ and $x=4$.

We need to solve $2x+3=0$ and $3x-1=0$. This means that we will have two different solutions for $x$.

$x=-\dfrac{3}{2}$ and $x=\dfrac{1}{3}$

Don't give mixed numbers!