Find the Domain -6x^2-5y=4x+3y

$- 6 x^{2} - 5 y = 4 x + 3 y$

Step 1

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

Subtract $3 y$ from both sides of the equation.

$- 6 x^{2} - 5 y - 3 y = 4 x$

Subtract $3 y$ from $- 5 y$ .

$- 6 x^{2} - 8 y = 4 x$

Step 2

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

$- 8 y = 4 x + 6 x^{2}$

Step 3

Divide each term in $- 8 y = 4 x + 6 x^{2}$ by $- 8$ and simplify.

Divide each term in $- 8 y = 4 x + 6 x^{2}$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{4 x}{- 8} + \frac{6 x^{2}}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{4 x}{- 8} + \frac{6 x^{2}}{- 8}$

Divide $y$ by $1$ .

$y = \frac{4 x}{- 8} + \frac{6 x^{2}}{- 8}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ and $- 8$ .

Factor $4$ out of $4 x$ .

$y = \frac{4 (x)}{- 8} + \frac{6 x^{2}}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

$y = \frac{4 x}{4 \cdot - 2} + \frac{6 x^{2}}{- 8}$

Cancel the common factor.

$y = \frac{4 x}{4 \cdot - 2} + \frac{6 x^{2}}{- 8}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Cancel the common factor of $6$ and $- 8$ .

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

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

Cancel the common factors.

Factor $2$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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^2-5y=4x+3y

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