\(a.3-4y+24+6y=y+27+3y\)
\(6y-4y-y-3y=27-24-3\)
\(-2y=0\Rightarrow y=0\)
\(b.5-\left(x-6\right)=4\left(3-2x\right)\)
\(5-x+6=12-8x\)
\(8x-x=12-6-5\)
\(7x=1\Rightarrow x=\frac{1}{7}\)
\(c.\left(x+1\right)\left(2x-3\right)=\left(2x-1\right)\left(x+5\right)\)
\(2x^2-3x+2x-3=2x^2+10x-x-5\)
\(\left(2x^2-2x^2\right)-\left(3x-2x+10x-x\right)=-5+3\)
\(-10x=-2\Rightarrow x=\frac{1}{5}\)
\(d.2x\left(x+2\right)^2-8x^2=2\left(x-2\right)\left(x^2+2x+4\right)\)
\(2x\left(x^2+4x+4\right)-8x^2=\left(2x-4\right)\left(x^2+2x+4\right)\)
\(2x^3+8x^2+8x-8x^2=2x^3+4x^2+8x-4x^2-8x-16\)
\(\left(2x^3-2x^3\right)+\left(8x^2-8x^2-4x^2+4x^2\right)+\left(8x-8x+8x\right)=-16\)
\(8x=-16\Rightarrow x=-2\)
\(e.\left(x-3\right)\left(x+4\right)-2\left(3x-2\right)=\left(x-4\right)^2\)
\(x^2+4x-3x-12-6x+4=x^2-8x+16\)
\(\left(x^2-x^2\right)+\left(4x-3x-6x+8x\right)=16-4+12\)
\(3x=24\Rightarrow x=8\)
\(f.\left(x+1\right)\left(x^2-x+1\right)-2x=x\left(x+1\right)\left(x-1\right)\)
\(x^3+1-2x=x\left(x^2-1\right)\)
\(\left(x^3-x^3\right)-\left(2x-x\right)=-1\)
\(-x=-1\Rightarrow x=1\)
