Solve y=-4^2(-x+3)(-4+1)(-4-x)(-4-3)

$$y = - 4 ^ { 2 } ( - x + 3 ) ( - 4 + 1 ) ( - 4 - x ) ( - 4 - 3 )$$

Solve for y

$$y=-336\left(x-3\right)\left(x+4\right)$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$y=-16\left(-x+3\right)\left(-4+1\right)\left(-4-x\right)\left(-4-3\right)$$

Add -4 and 1 to get -3.

$$y=-16\left(-x+3\right)\left(-3\right)\left(-4-x\right)\left(-4-3\right)$$

Multiply -16 and -3 to get 48.

$$y=48\left(-x+3\right)\left(-4-x\right)\left(-4-3\right)$$

Subtract 3 from -4 to get -7.

$$y=48\left(-x+3\right)\left(-4-x\right)\left(-7\right)$$

Multiply 48 and -7 to get -336.

$$y=-336\left(-x+3\right)\left(-4-x\right)$$

Use the distributive property to multiply -336 by -x+3.

$$y=\left(-336\left(-x\right)-1008\right)\left(-4-x\right)$$

Multiply -336 and -1 to get 336.

$$y=\left(336x-1008\right)\left(-4-x\right)$$

Use the distributive property to multiply 336x-1008 by -4-x and combine like terms.

$$y=-336x-336x^{2}+4032$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{86436-21y}}{84}-\frac{1}{2}$$

$$x=\frac{\sqrt{86436-21y}}{84}-\frac{1}{2}$$

Solve for x

$$x=\frac{\sqrt{86436-21y}}{84}-\frac{1}{2}$$

$$x=-\frac{\sqrt{86436-21y}}{84}-\frac{1}{2}\text{, }y\leq 4116$$