Solve y-(-3)=-3/2(x-(-4x^2)]

$$y - ( - 3 ) = - \frac { 3 } { 2 } ( x - ( - 4 x ^ { 2 } ) ]$$

Solve for y

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

Solution Steps

The opposite of -3 is 3.

$$y+3=-\frac{3}{2}\left(x-\left(-4x^{2}\right)\right)$$

The opposite of -4x^{2} is 4x^{2}.

$$y+3=-\frac{3}{2}\left(x+4x^{2}\right)$$

Use the distributive property to multiply -\frac{3}{2} by x+4x^{2}.

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

Subtract 3 from both sides.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{-96y-279}}{24}-\frac{1}{8}$$

$$x=-\frac{\sqrt{-96y-279}}{24}-\frac{1}{8}$$

Solve for x

$$x=\frac{\sqrt{-96y-279}}{24}-\frac{1}{8}$$

$$x=-\frac{\sqrt{-96y-279}}{24}-\frac{1}{8}\text{, }y\leq -\frac{93}{32}$$