Precalculus Examples

$y^{2} + 3 y z - 8 z - 4 x = 0$

Step 1

Move all terms not containing $z$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $y^{2}$ from both sides of the equation.

$3 y z - 8 z - 4 x = - y^{2}$

Step 1.2

Add $4 x$ to both sides of the equation.

$3 y z - 8 z = - y^{2} + 4 x$

Step 2

Factor $z$ out of $3 y z - 8 z$ .

Tap for more steps...

Step 2.1

Factor $z$ out of $3 y z$ .

$z (3 y) - 8 z = - y^{2} + 4 x$

Step 2.2

Factor $z$ out of $- 8 z$ .

$z (3 y) + z \cdot - 8 = - y^{2} + 4 x$

Step 2.3

Factor $z$ out of $z (3 y) + z \cdot - 8$ .

$z (3 y - 8) = - y^{2} + 4 x$

Step 3

Divide each term in $z (3 y - 8) = - y^{2} + 4 x$ by $3 y - 8$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $z (3 y - 8) = - y^{2} + 4 x$ by $3 y - 8$ .

$\frac{z (3 y - 8)}{3 y - 8} = \frac{- y^{2}}{3 y - 8} + \frac{4 x}{3 y - 8}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $3 y - 8$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{z (3 y - 8)}{3 y - 8} = \frac{- y^{2}}{3 y - 8} + \frac{4 x}{3 y - 8}$

Step 3.2.1.2

Divide $z$ by $1$ .

$z = \frac{- y^{2}}{3 y - 8} + \frac{4 x}{3 y - 8}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Move the negative in front of the fraction.

$z = - \frac{y^{2}}{3 y - 8} + \frac{4 x}{3 y - 8}$

Step 3.3.2

Combine the numerators over the common denominator.

$z = \frac{- y^{2} + 4 x}{3 y - 8}$

Step 3.3.3

Factor $- 1$ out of $- y^{2}$ .

$z = \frac{- (y^{2}) + 4 x}{3 y - 8}$

Step 3.3.4

Factor $- 1$ out of $4 x$ .

$z = \frac{- (y^{2}) - (- 4 x)}{3 y - 8}$

Step 3.3.5

Factor $- 1$ out of $- (y^{2}) - (- 4 x)$ .

$z = \frac{- (y^{2} - 4 x)}{3 y - 8}$

Step 3.3.6

Simplify the expression.

Tap for more steps...

Step 3.3.6.1

Rewrite $- (y^{2} - 4 x)$ as $- 1 (y^{2} - 4 x)$ .

$z = \frac{- 1 (y^{2} - 4 x)}{3 y - 8}$

Step 3.3.6.2

Move the negative in front of the fraction.

$z = - \frac{y^{2} - 4 x}{3 y - 8}$