p.lazarov06 wrote: Solve the equation: \[4x^2+|9-6x|=|10x-15|+6(2x+1)\] $\iff$ Either $x\ge \frac 32$ and $4x^2+(6x-9)=(10x-15)+12x+6$ which is $4x^2-16x=0$ and so $x=4$ Either $x<\frac 32$ and $4x^2-(6x-9)=-(10x-15)+12x+6$ which is $4x^2-8x-12=0$ and so $x=-1$ And solutions $\boxed{x\in\{-1,4\}}$