Algebra Examples

$2 y (y - 2) = (y + 1) (y - 6) - 2$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $2 y (y - 2)$ .

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Step 1.1.1.1

Apply the distributive property.

$2 y \cdot y + 2 y \cdot - 2 = (y + 1) (y - 6) - 2$

Step 1.1.1.2

Multiply $y$ by $y$ by adding the exponents.

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Step 1.1.1.2.1

Move $y$ .

$2 (y \cdot y) + 2 y \cdot - 2 = (y + 1) (y - 6) - 2$

Step 1.1.1.2.2

Multiply $y$ by $y$ .

$2 y^{2} + 2 y \cdot - 2 = (y + 1) (y - 6) - 2$

Step 1.1.1.3

Multiply $- 2$ by $2$ .

$2 y^{2} - 4 y = (y + 1) (y - 6) - 2$

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $(y + 1) (y - 6) - 2$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Expand $(y + 1) (y - 6)$ using the FOIL Method.

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Step 1.2.1.1.1.1

Apply the distributive property.

$2 y^{2} - 4 y = y (y - 6) + 1 (y - 6) - 2$

Step 1.2.1.1.1.2

Apply the distributive property.

$2 y^{2} - 4 y = y \cdot y + y \cdot - 6 + 1 (y - 6) - 2$

Step 1.2.1.1.1.3

Apply the distributive property.

$2 y^{2} - 4 y = y \cdot y + y \cdot - 6 + 1 y + 1 \cdot - 6 - 2$

Step 1.2.1.1.2

Simplify and combine like terms.

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Step 1.2.1.1.2.1

Simplify each term.

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Step 1.2.1.1.2.1.1

Multiply $y$ by $y$ .

$2 y^{2} - 4 y = y^{2} + y \cdot - 6 + 1 y + 1 \cdot - 6 - 2$

Step 1.2.1.1.2.1.2

Move $- 6$ to the left of $y$ .

$2 y^{2} - 4 y = y^{2} - 6 \cdot y + 1 y + 1 \cdot - 6 - 2$

Step 1.2.1.1.2.1.3

Multiply $y$ by $1$ .

$2 y^{2} - 4 y = y^{2} - 6 y + y + 1 \cdot - 6 - 2$

Step 1.2.1.1.2.1.4

Multiply $- 6$ by $1$ .

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

Step 1.2.1.1.2.2

Add $- 6 y$ and $y$ .

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

Step 1.2.1.2

Subtract $2$ from $- 6$ .

$2 y^{2} - 4 y = y^{2} - 5 y - 8$

Step 1.3

Move all the expressions to the left side of the equation.

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Step 1.3.1

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

$2 y^{2} - 4 y - y^{2} = - 5 y - 8$

Step 1.3.2

Add $5 y$ to both sides of the equation.

$2 y^{2} - 4 y - y^{2} + 5 y = - 8$

Step 1.3.3

Add $8$ to both sides of the equation.

$2 y^{2} - 4 y - y^{2} + 5 y + 8 = 0$

Step 1.4

Simplify $2 y^{2} - 4 y - y^{2} + 5 y + 8$ .

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Step 1.4.1

Subtract $y^{2}$ from $2 y^{2}$ .

$y^{2} - 4 y + 5 y + 8 = 0$

Step 1.4.2

Add $- 4 y$ and $5 y$ .

$y^{2} + y + 8 = 0$

Step 2

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

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

Step 3

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 1$ , $b = 1$ , $c = 8$