a) \(2{x^3} + 6{x^2} = {x^2} + 3x\)

\(\Leftrightarrow 2x^2(x+3)=x(x+3)\)

\(\Leftrightarrow 2x^2(x+3)-x(x+3)=0\)

\(\Leftrightarrow (2x^2-x)(x+3)=0\)

\(\Leftrightarrow x(2x-1)(x+3)=0\)

\(\Leftrightarrow \left[ \matrix{x=0 \hfill \cr 2x-1=0 \hfill \cr x+3=0 \hfill \cr} \right.\)

\(\Leftrightarrow \left[ \matrix{x=0 \hfill \cr x=\frac{1}{2} \hfill \cr x=-3 \hfill \cr} \right.\)

Vậy phương trình có tập nghiệm là \(S=\left \{ 0; \frac{1}{2}; -3 \right \}\)

b) \(\left( {3x - 1} \right)\left( {{x^2} + 2} \right) = \left( {3x - 1} \right)\left( {7x - 10} \right)\)

\(\Leftrightarrow (3x-1)(x^2+2)-(3x-1)(7x-10)=0\)

\(\Leftrightarrow (3x-1)(x^2+2-7x+10)=0\)

\(\Leftrightarrow (3x-1)(x^2-7x+12)=0\)

\(\Leftrightarrow (3x-1)(x^2-3x-4x+12)=0\)

\(\Leftrightarrow (3x-1)[x(x-3)-4(x-3)]=0\)

\(\Leftrightarrow (3x-1)(x-4)(x-3)=0\)

\(\Leftrightarrow \left[ \matrix{3x-1=0 \hfill \cr x-4=0 \hfill \cr x-3=0 \hfill \cr} \right.\)

\(\Leftrightarrow \left[ \matrix{x=\frac{1}{3} \hfill \cr x=4 \hfill \cr x=3 \hfill \cr} \right.\)

Vậy phương trình có tập nghiệm là \(S=\left \{ 3; \frac{1}{3}; 4 \right \}\)