How to solve 3(x)^(2)-2y=6

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 3(x)^(2)-2y=6 | Equatix

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$$3 { x }^{ 2 } -2y=6$$

$y=\frac{3\left(x^{2}-2\right)}{2}$

Subtract $3x^{2}$ from both sides.

$$-2y=6-3x^{2}$$

Divide both sides by $-2$.

$$\frac{-2y}{-2}=\frac{6-3x^{2}}{-2}$$

Dividing by $-2$ undoes the multiplication by $-2$.

$$y=\frac{6-3x^{2}}{-2}$$

Divide $6-3x^{2}$ by $-2$.

$$y=\frac{3x^{2}}{2}-3$$

$x=-\frac{\sqrt{6\left(y+3\right)}}{3}$
$x=\frac{\sqrt{6\left(y+3\right)}}{3}$

$x=\frac{\sqrt{6\left(y+3\right)}}{3}$
$x=-\frac{\sqrt{6\left(y+3\right)}}{3}\text{, }y\geq -3$