Solve y=8*(x^2-4)+5*(x-2)

$$y=8 \times ( { x }^{ 2 } -4)+5 \times (x-2)$$

Solve for y

$$y=\left(x-2\right)\left(8x+21\right)$$

Solution Steps

Use the distributive property to multiply 8 by x^{2}-4.

$$y=8x^{2}-32+5\left(x-2\right)$$

Use the distributive property to multiply 5 by x-2.

$$y=8x^{2}-32+5x-10$$

Subtract 10 from -32 to get -42.

$$y=8x^{2}-42+5x$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{32y+1369}-5}{16}$$

$$x=\frac{\sqrt{32y+1369}-5}{16}$$

Solve for x

$$x=\frac{-\sqrt{32y+1369}-5}{16}$$

$$x=\frac{\sqrt{32y+1369}-5}{16}\text{, }y\geq -\frac{1369}{32}$$