Algebra Examples

6 {(x - 2)}^{2} + 3 y = 3

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

Step 1

Subtract

6 {(x - 2)}^{2}

$6 {(x - 2)}^{2}$ from both sides of the equation.

3 y = 3 - 6 {(x - 2)}^{2}

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

Step 2

Divide each term in

3 y = 3 - 6 {(x - 2)}^{2}

$3 y = 3 - 6 {(x - 2)}^{2}$ by

3

$3$ and simplify.

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Step 2.1

Divide each term in

3 y = 3 - 6 {(x - 2)}^{2}

$3 y = 3 - 6 {(x - 2)}^{2}$ by

3

$3$ .

\frac{3 y}{3} = \frac{3}{3} + \frac{- 6 {(x - 2)}^{2}}{3}

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

3

$3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide

$y$ by

$1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide

$3$ by

$3$ .

$y = 1 + \frac{- 6 {(x - 2)}^{2}}{3}$

Step 2.3.1.2

Cancel the common factor of

$- 6$ and

$3$ .

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Step 2.3.1.2.1

Factor

$3$ out of

$- 6 {(x - 2)}^{2}$ .

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

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor

$3$ out of

$3$ .

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

Step 2.3.1.2.2.2

Cancel the common factor.

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

Step 2.3.1.2.2.3

Rewrite the expression.

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

Step 2.3.1.2.2.4

Divide

$- 2 {(x - 2)}^{2}$ by

$1$ .

$y = 1 - 2 {(x - 2)}^{2}$

Step 3

Reorder terms.

$y = - 2 {(x - 2)}^{2} + 1$

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