Question

1. $3x^2 - 2 = -x$

Explanation:

Step1: Rearrange to standard quadratic form

Move all terms to one side to get $3x^2 + x - 2 = 0$.

Step2: Factor the quadratic expression

Find two numbers that multiply to $3\times(-2)=-6$ and add to $1$. The numbers are $3$ and $-2$. Split the middle term and factor:

$$\begin{align*} 3x^2 + 3x - 2x - 2 &= 0\\ 3x(x+1) - 2(x+1) &= 0\\ (3x - 2)(x + 1) &= 0 \end{align*}$$

Step3: Solve for $x$

Set each factor equal to zero:
$3x - 2 = 0$ or $x + 1 = 0$

Answer:

$x=\frac{2}{3}$ or $x=-1$