Find the Domain -6x^2+x+5y=-6y

$- 6 x^{2} + x + 5 y = - 6 y$

Step 1

Move all terms containing $y$ to the left side of the equation.

Add $6 y$ to both sides of the equation.

$- 6 x^{2} + x + 5 y + 6 y = 0$

Add $5 y$ and $6 y$ .

$- 6 x^{2} + x + 11 y = 0$

Step 2

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

Add $6 x^{2}$ to both sides of the equation.

$x + 11 y = 6 x^{2}$

Subtract $x$ from both sides of the equation.

$11 y = 6 x^{2} - x$

Step 3

Divide each term in $11 y = 6 x^{2} - x$ by $11$ and simplify.

Divide each term in $11 y = 6 x^{2} - x$ by $11$ .

$\frac{11 y}{11} = \frac{6 x^{2}}{11} + \frac{- x}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{6 x^{2}}{11} + \frac{- x}{11}$

Divide $y$ by $1$ .

$y = \frac{6 x^{2}}{11} + \frac{- x}{11}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{6 x^{2}}{11} - \frac{x}{11}$

Step 4

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 5

Find the Domain -6x^2+x+5y=-6y

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