Finite Math Examples

$3 (y - 1) = (y + 2) (y - 3) - (y + 3) (y - 5)$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$(y + 2) (y - 3) - (y + 3) (y - 5) = 3 (y - 1)$

Step 2

Simplify $(y + 2) (y - 3) - (y + 3) (y - 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Expand $(y + 2) (y - 3)$ using the FOIL Method.

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Step 2.1.1.1

Apply the distributive property.

$y (y - 3) + 2 (y - 3) - (y + 3) (y - 5) = 3 (y - 1)$

Step 2.1.1.2

Apply the distributive property.

$y \cdot y + y \cdot - 3 + 2 (y - 3) - (y + 3) (y - 5) = 3 (y - 1)$

Step 2.1.1.3

Apply the distributive property.

$y \cdot y + y \cdot - 3 + 2 y + 2 \cdot - 3 - (y + 3) (y - 5) = 3 (y - 1)$

Step 2.1.2

Simplify and combine like terms.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

Multiply $y$ by $y$ .

$y^{2} + y \cdot - 3 + 2 y + 2 \cdot - 3 - (y + 3) (y - 5) = 3 (y - 1)$

Step 2.1.2.1.2

Move $- 3$ to the left of $y$ .

$y^{2} - 3 \cdot y + 2 y + 2 \cdot - 3 - (y + 3) (y - 5) = 3 (y - 1)$

Step 2.1.2.1.3

Multiply $2$ by $- 3$ .

$y^{2} - 3 y + 2 y - 6 - (y + 3) (y - 5) = 3 (y - 1)$

Step 2.1.2.2

Add $- 3 y$ and $2 y$ .

$y^{2} - y - 6 - (y + 3) (y - 5) = 3 (y - 1)$

Step 2.1.3

Apply the distributive property.

$y^{2} - y - 6 + (- y - 1 \cdot 3) (y - 5) = 3 (y - 1)$

Step 2.1.4

Multiply $- 1$ by $3$ .

$y^{2} - y - 6 + (- y - 3) (y - 5) = 3 (y - 1)$

Step 2.1.5

Expand $(- y - 3) (y - 5)$ using the FOIL Method.

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Step 2.1.5.1

Apply the distributive property.

$y^{2} - y - 6 - y (y - 5) - 3 (y - 5) = 3 (y - 1)$

Step 2.1.5.2

Apply the distributive property.

$y^{2} - y - 6 - y \cdot y - y \cdot - 5 - 3 (y - 5) = 3 (y - 1)$

Step 2.1.5.3

Apply the distributive property.

$y^{2} - y - 6 - y \cdot y - y \cdot - 5 - 3 y - 3 \cdot - 5 = 3 (y - 1)$

Step 2.1.6

Simplify and combine like terms.

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Step 2.1.6.1

Simplify each term.

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Step 2.1.6.1.1

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

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Step 2.1.6.1.1.1

Move $y$ .

$y^{2} - y - 6 - (y \cdot y) - y \cdot - 5 - 3 y - 3 \cdot - 5 = 3 (y - 1)$

Step 2.1.6.1.1.2

Multiply $y$ by $y$ .

$y^{2} - y - 6 - y^{2} - y \cdot - 5 - 3 y - 3 \cdot - 5 = 3 (y - 1)$

Step 2.1.6.1.2

Multiply $- 5$ by $- 1$ .

$y^{2} - y - 6 - y^{2} + 5 y - 3 y - 3 \cdot - 5 = 3 (y - 1)$

Step 2.1.6.1.3

Multiply $- 3$ by $- 5$ .

$y^{2} - y - 6 - y^{2} + 5 y - 3 y + 15 = 3 (y - 1)$

Step 2.1.6.2

Subtract $3 y$ from $5 y$ .

$y^{2} - y - 6 - y^{2} + 2 y + 15 = 3 (y - 1)$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Combine the opposite terms in $y^{2} - y - 6 - y^{2} + 2 y + 15$ .

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Step 2.2.1.1

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

$- y - 6 + 0 + 2 y + 15 = 3 (y - 1)$

Step 2.2.1.2

Add $- y - 6$ and $0$ .

$- y - 6 + 2 y + 15 = 3 (y - 1)$

Step 2.2.2

Add $- y$ and $2 y$ .

$y - 6 + 15 = 3 (y - 1)$

Step 2.2.3

Add $- 6$ and $15$ .

$y + 9 = 3 (y - 1)$

Step 3

Simplify $3 (y - 1)$ .

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Step 3.1

Apply the distributive property.

$y + 9 = 3 y + 3 \cdot - 1$

Step 3.2

Multiply $3$ by $- 1$ .

$y + 9 = 3 y - 3$

Step 4

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

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Step 4.1

Subtract $3 y$ from both sides of the equation.

$y + 9 - 3 y = - 3$

Step 4.2

Subtract $3 y$ from $y$ .

$- 2 y + 9 = - 3$

Step 5

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

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Step 5.1

Subtract $9$ from both sides of the equation.

$- 2 y = - 3 - 9$

Step 5.2

Subtract $9$ from $- 3$ .

$- 2 y = - 12$

Step 6

Divide each term in $- 2 y = - 12$ by $- 2$ and simplify.

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Step 6.1

Divide each term in $- 2 y = - 12$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 12}{- 2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 12$ by $- 2$ .

$y = 6$