\(12x^3+16x^2-5x-3=12x^3+12x^2-9x+4x^2+4x-3\)
\(=3x\left(4x^2+4x-3\right)+\left(4x^2+4x-3\right)\)
\(=\left(3x+1\right)\left(4x^2+4x-3\right)=\left(3x+1\right)\left(4x^2+6x-2x-3\right)\)
\(=\left(3x+1\right)\left(2x\left(2x+3\right)-\left(2x+3\right)\right)\)
\(=\left(3x+1\right)\left(2x-1\right)\left(2x+3\right)\)