Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Add $- 2 y$ and $6 y$ .

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

Step 2

Add $3 x^{2}$ to both sides of the equation.

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

Step 3

Divide each term in $4 y = - 6 x + 3 x^{2}$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 y = - 6 x + 3 x^{2}$ by $4$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $y$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

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

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Step 3.3.1.1.1

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

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

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $2$ out of $4$ .

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

Step 3.3.1.1.2.2

Cancel the common factor.

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

Step 3.3.1.1.2.3

Rewrite the expression.

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

Step 3.3.1.2

Move the negative in front of the fraction.

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

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

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