O/N 17/P22/Q5/b,c (a) Solve $$ 2 x(x+1)=3(4-x) $$.

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Solve the equation $$ 2x(x+1)=3(4-x) $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$2x\left(x+1ight)=3\left(4-xight)$$
- step1: Expand the expression:
  $$2x^{2}+2x=12-3x$$
- step2: Move the expression to the left side:
  $$2x^{2}+5x-12=0$$
- step3: Factor the expression:
  $$\left(x+4ight)\left(2x-3ight)=0$$
- step4: Separate into possible cases:
  $$\begin{align}&2x-3=0\&x+4=0\end{align}$$
- step5: Solve the equation:
  $$\begin{align}&x=\frac{3}{2}\&x=-4\end{align}$$
- step6: Rewrite:
  $$x_{1}=-4,x_{2}=\frac{3}{2}$$
The solutions to the equation $$2x(x+1)=3(4-x)$$ are $$x=-4$$ and $$x=\frac{3}{2}$$ or $$x=1.5$$.
The solutions are $$x = -4$$ and $$x = 1.5$$.

O/N 17/P22/Q5/b,c
(a) Solve .

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O/N 17/P22/Q5/b,c (a) Solve .