Solve (x-4)(-20x+250)=-20(x^2-33/4)+y

$$(x-4)(-20x+250)=-20( { x }^{ 2 } - \frac{ 33 }{ 4 } )+y$$

Solve for x

$$x=\frac{y+1165}{330}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-4 by -20x+250 and combine like terms.

$$-20x^{2}+330x-1000=-20\left(x^{2}-\frac{33}{4}\right)+y$$

Use the distributive property to multiply -20 by x^{2}-\frac{33}{4}.

$$-20x^{2}+330x-1000=-20x^{2}+165+y$$

Add 20x^{2} to both sides.

$$-20x^{2}+330x-1000+20x^{2}=165+y$$

Combine -20x^{2} and 20x^{2} to get 0.

$$330x-1000=165+y$$

Add 1000 to both sides.

$$330x=165+y+1000$$

Add 165 and 1000 to get 1165.

$$330x=1165+y$$

The equation is in standard form.

$$330x=y+1165$$

Divide both sides by 330.

$$\frac{330x}{330}=\frac{y+1165}{330}$$

Dividing by 330 undoes the multiplication by 330.

$$x=\frac{y+1165}{330}$$

Divide 1165+y by 330.

$$x=\frac{y}{330}+\frac{233}{66}$$

Solve for y

$$y=330x-1165$$

Solution Steps

Use the distributive property to multiply x-4 by -20x+250 and combine like terms.

$$-20x^{2}+330x-1000=-20\left(x^{2}-\frac{33}{4}\right)+y$$

Use the distributive property to multiply -20 by x^{2}-\frac{33}{4}.

$$-20x^{2}+330x-1000=-20x^{2}+165+y$$

Swap sides so that all variable terms are on the left hand side.

$$-20x^{2}+165+y=-20x^{2}+330x-1000$$

Add 20x^{2} to both sides.

$$165+y=-20x^{2}+330x-1000+20x^{2}$$

Combine -20x^{2} and 20x^{2} to get 0.

$$165+y=330x-1000$$

Subtract 165 from both sides.

$$y=330x-1000-165$$

Subtract 165 from -1000 to get -1165.

$$y=330x-1165$$