Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $2 y$ from both sides of the equation.

$- 4 x^{2} - 3 x + y - 2 y = 0$

Step 1.2

Subtract $2 y$ from $y$ .

$- 4 x^{2} - 3 x - y = 0$

Step 2

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

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Step 2.1

Add $4 x^{2}$ to both sides of the equation.

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

Step 2.2

Add $3 x$ to both sides of the equation.

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

Step 3

Divide each term in $- y = 4 x^{2} + 3 x$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = 4 x^{2} + 3 x$ by $- 1$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

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

Step 3.2.2

Divide $y$ by $1$ .

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

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

Move the negative one from the denominator of $\frac{4 x^{2}}{- 1}$ .

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

Step 3.3.1.2

Rewrite $- 1 \cdot (4 x^{2})$ as $- (4 x^{2})$ .

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

Step 3.3.1.3

Multiply $4$ by $- 1$ .

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

Step 3.3.1.4

Move the negative one from the denominator of $\frac{3 x}{- 1}$ .

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

Step 3.3.1.5

Rewrite $- 1 \cdot (3 x)$ as $- (3 x)$ .

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

Step 3.3.1.6

Multiply $3$ by $- 1$ .

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

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.

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