Solve for k x=3y^2+ky

$x = 3 y^{2} + k y$

Step 1

Rewrite the equation as $3 y^{2} + k y = x$ .

$3 y^{2} + k y = x$

Step 2

Subtract $3 y^{2}$ from both sides of the equation.

$k y = x - 3 y^{2}$

Step 3

Divide each term in $k y = x - 3 y^{2}$ by $y$ and simplify.

Divide each term in $k y = x - 3 y^{2}$ by $y$ .

$\frac{k y}{y} = \frac{x}{y} + \frac{- 3 y^{2}}{y}$

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{k y}{y} = \frac{x}{y} + \frac{- 3 y^{2}}{y}$

Divide $k$ by $1$ .

$k = \frac{x}{y} + \frac{- 3 y^{2}}{y}$

Simplify the right side.

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

Factor $y$ out of $- 3 y^{2}$ .

$k = \frac{x}{y} + \frac{y (- 3 y)}{y}$

Cancel the common factors.

Raise $y$ to the power of $1$ .

$k = \frac{x}{y} + \frac{y (- 3 y)}{y^{1}}$

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

$k = \frac{x}{y} + \frac{y (- 3 y)}{y \cdot 1}$

Cancel the common factor.

$k = \frac{x}{y} + \frac{y (- 3 y)}{y \cdot 1}$

Rewrite the expression.

$k = \frac{x}{y} + \frac{- 3 y}{1}$

Divide $- 3 y$ by $1$ .

$k = \frac{x}{y} - 3 y$