Write in Standard Form x^2+6x+4y+13=0

$x^{2} + 6 x + 4 y + 13 = 0$

Solve for $y$ .

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

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

$6 x + 4 y + 13 = - x^{2}$

Subtract $6 x$ from both sides of the equation.

$4 y + 13 = - x^{2} - 6 x$

Subtract $13$ from both sides of the equation.

$4 y = - x^{2} - 6 x - 13$

Divide each term in $4 y = - x^{2} - 6 x - 13$ by $4$ and simplify.

Divide each term in $4 y = - x^{2} - 6 x - 13$ by $4$ .

$\frac{4 y}{4} = \frac{- x^{2}}{4} + \frac{- 6 x}{4} + \frac{- 13}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- x^{2}}{4} + \frac{- 6 x}{4} + \frac{- 13}{4}$

Divide $y$ by $1$ .

$y = \frac{- x^{2}}{4} + \frac{- 6 x}{4} + \frac{- 13}{4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{4} + \frac{- 6 x}{4} + \frac{- 13}{4}$

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6 x$ .

$y = - \frac{x^{2}}{4} + \frac{2 (- 3 x)}{4} + \frac{- 13}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = - \frac{x^{2}}{4} + \frac{2 (- 3 x)}{2 (2)} + \frac{- 13}{4}$

Cancel the common factor.

$y = - \frac{x^{2}}{4} + \frac{2 (- 3 x)}{2 \cdot 2} + \frac{- 13}{4}$

Rewrite the expression.

$y = - \frac{x^{2}}{4} + \frac{- 3 x}{2} + \frac{- 13}{4}$

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{4} - \frac{(3) x}{2} + \frac{- 13}{4}$

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{4} - \frac{3 x}{2} - \frac{13}{4}$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Reorder terms.

$y = - (\frac{1}{4} x^{2}) - (\frac{3}{2} x) - \frac{13}{4}$

Remove parentheses.

$y = - \frac{1}{4} x^{2} - (\frac{3}{2} x) - \frac{13}{4}$

Remove parentheses.

$y = - \frac{1}{4} x^{2} - \frac{3}{2} x - \frac{13}{4}$