Solve the inequality \(\left(2 x^2+3 x\right)(1-x) \geqslant 0\), expressing your answer in set notation. (3 marks)
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\(\left(2 x^2+3 x\right)(1-x)=x(2 x+3)(1-x)\)
\(x(2 x+3)(1-x) \geqslant 0\)
\(\text{Zeros at} \ \ x=0, x=-\dfrac{3}{2} \ \ \text{and} \ \ x=1\)
\(\text{At} \ \ x=-1: \ (-1)(1)(2)<0\)
\(\therefore \text{Graph} \geqslant 0 \ \ \text{for} \ \ x \in\left(-\infty,-\dfrac{3}{2}\right]\ \cup\ x \in [0,1] \)