\(\left(x+3\right)\left(x-4\right)-x\left(x-3\right)=12\)
\(\Rightarrow x\left(x-4\right)+3\left(x-4\right)-x\left(x-3\right)=12\)
\(\Rightarrow x^2-4x+3x-12-x^2+3x=12\)
\(\Rightarrow\left(x^2-x^2\right)+\left(3x+3x-4x\right)-12=12\)
\(\Rightarrow2x-12=12\)
\(\Rightarrow2x=24\Rightarrow x=12\)