Solve y=(4x-1)(36-x^2)+2x(2x^2-x-62)

$$y=(4x-1)(36- { x }^{ 2 } )+2x(2 { x }^{ 2 } -x-62)$$

Solve for y

$$y=-\left(x-18\right)\left(x-2\right)$$

Solution Steps

Use the distributive property to multiply 4x-1 by 36-x^{2}.

$$y=144x-4x^{3}-36+x^{2}+2x\left(2x^{2}-x-62\right)$$

Use the distributive property to multiply 2x by 2x^{2}-x-62.

$$y=144x-4x^{3}-36+x^{2}+4x^{3}-2x^{2}-124x$$

Combine -4x^{3} and 4x^{3} to get 0.

$$y=144x-36+x^{2}-2x^{2}-124x$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$y=144x-36-x^{2}-124x$$

Combine 144x and -124x to get 20x.

$$y=20x-36-x^{2}$$

Solve for x (complex solution)

$$x=\sqrt{64-y}+10$$

$$x=-\sqrt{64-y}+10$$

Solve for x

$$x=\sqrt{64-y}+10$$

$$x=-\sqrt{64-y}+10\text{, }y\leq 64$$