Precalculus Examples

$6 x^{2} + 24 x + 2 y - 10 = 0$

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

Subtract $6 x^{2}$ from both sides of the equation.

$24 x + 2 y - 10 = - 6 x^{2}$

Step 1.1.2

Subtract $24 x$ from both sides of the equation.

$2 y - 10 = - 6 x^{2} - 24 x$

Step 1.1.3

Add $10$ to both sides of the equation.

$2 y = - 6 x^{2} - 24 x + 10$

Step 1.2

Divide each term in $2 y = - 6 x^{2} - 24 x + 10$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 y = - 6 x^{2} - 24 x + 10$ by $2$ .

$\frac{2 y}{2} = \frac{- 6 x^{2}}{2} + \frac{- 24 x}{2} + \frac{10}{2}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 6 x^{2}}{2} + \frac{- 24 x}{2} + \frac{10}{2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6 x^{2}}{2} + \frac{- 24 x}{2} + \frac{10}{2}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Cancel the common factor of $- 6$ and $2$ .

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Step 1.2.3.1.1.1

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

$y = \frac{2 (- 3 x^{2})}{2} + \frac{- 24 x}{2} + \frac{10}{2}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (- 3 x^{2})}{2 (1)} + \frac{- 24 x}{2} + \frac{10}{2}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (- 3 x^{2})}{2 \cdot 1} + \frac{- 24 x}{2} + \frac{10}{2}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{- 3 x^{2}}{1} + \frac{- 24 x}{2} + \frac{10}{2}$

Step 1.2.3.1.1.2.4

Divide $- 3 x^{2}$ by $1$ .

$y = - 3 x^{2} + \frac{- 24 x}{2} + \frac{10}{2}$

Step 1.2.3.1.2

Cancel the common factor of $- 24$ and $2$ .

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Step 1.2.3.1.2.1

Factor $2$ out of $- 24 x$ .

$y = - 3 x^{2} + \frac{2 (- 12 x)}{2} + \frac{10}{2}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $2$ out of $2$ .

$y = - 3 x^{2} + \frac{2 (- 12 x)}{2 (1)} + \frac{10}{2}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = - 3 x^{2} + \frac{2 (- 12 x)}{2 \cdot 1} + \frac{10}{2}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = - 3 x^{2} + \frac{- 12 x}{1} + \frac{10}{2}$

Step 1.2.3.1.2.2.4

Divide $- 12 x$ by $1$ .

$y = - 3 x^{2} - 12 x + \frac{10}{2}$

Step 1.2.3.1.3

Divide $10$ by $2$ .

$y = - 3 x^{2} - 12 x + 5$

Step 2

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

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

Step 3

The standard form is $- 3 x^{2} - 12 x + 5$ .

$y = - 3 x^{2} - 12 x + 5$

Step 4