Solve for x 16xy^2-y^6=8

$16 x y^{2} - y^{6} = 8$

Step 1

Add $y^{6}$ to both sides of the equation.

$16 x y^{2} = 8 + y^{6}$

Step 2

Divide each term in $16 x y^{2} = 8 + y^{6}$ by $16 y^{2}$ and simplify.

Divide each term in $16 x y^{2} = 8 + y^{6}$ by $16 y^{2}$ .

$\frac{16 x y^{2}}{16 y^{2}} = \frac{8}{16 y^{2}} + \frac{y^{6}}{16 y^{2}}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x y^{2}}{16 y^{2}} = \frac{8}{16 y^{2}} + \frac{y^{6}}{16 y^{2}}$

Rewrite the expression.

$\frac{x y^{2}}{y^{2}} = \frac{8}{16 y^{2}} + \frac{y^{6}}{16 y^{2}}$

Cancel the common factor of $y^{2}$ .

Cancel the common factor.

$\frac{x y^{2}}{y^{2}} = \frac{8}{16 y^{2}} + \frac{y^{6}}{16 y^{2}}$

Divide $x$ by $1$ .

$x = \frac{8}{16 y^{2}} + \frac{y^{6}}{16 y^{2}}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $8$ and $16$ .

Factor $8$ out of $8$ .

$x = \frac{8 (1)}{16 y^{2}} + \frac{y^{6}}{16 y^{2}}$

Cancel the common factors.

Factor $8$ out of $16 y^{2}$ .

$x = \frac{8 (1)}{8 (2 y^{2})} + \frac{y^{6}}{16 y^{2}}$

Cancel the common factor.

$x = \frac{8 \cdot 1}{8 (2 y^{2})} + \frac{y^{6}}{16 y^{2}}$

Rewrite the expression.

$x = \frac{1}{2 y^{2}} + \frac{y^{6}}{16 y^{2}}$

Cancel the common factor of $y^{6}$ and $y^{2}$ .

Factor $y^{2}$ out of $y^{6}$ .

$x = \frac{1}{2 y^{2}} + \frac{y^{2} y^{4}}{16 y^{2}}$

Cancel the common factors.

Factor $y^{2}$ out of $16 y^{2}$ .

$x = \frac{1}{2 y^{2}} + \frac{y^{2} y^{4}}{y^{2} \cdot 16}$

Cancel the common factor.

$x = \frac{1}{2 y^{2}} + \frac{y^{2} y^{4}}{y^{2} \cdot 16}$

Rewrite the expression.

$x = \frac{1}{2 y^{2}} + \frac{y^{4}}{16}$