Basic Math Examples

$45 = (y + 6) (y - 6)$

Step 1

Rewrite the equation as $(y + 6) (y - 6) = 45$ .

$(y + 6) (y - 6) = 45$

Step 2

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

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Step 2.1

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

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Step 2.1.1

Apply the distributive property.

$y (y - 6) + 6 (y - 6) = 45$

Step 2.1.2

Apply the distributive property.

$y \cdot y + y \cdot - 6 + 6 (y - 6) = 45$

Step 2.1.3

Apply the distributive property.

$y \cdot y + y \cdot - 6 + 6 y + 6 \cdot - 6 = 45$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the opposite terms in $y \cdot y + y \cdot - 6 + 6 y + 6 \cdot - 6$ .

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Step 2.2.1.1

Reorder the factors in the terms $y \cdot - 6$ and $6 y$ .

$y \cdot y - 6 y + 6 y + 6 \cdot - 6 = 45$

Step 2.2.1.2

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

$y \cdot y + 0 + 6 \cdot - 6 = 45$

Step 2.2.1.3

Add $y \cdot y$ and $0$ .

$y \cdot y + 6 \cdot - 6 = 45$

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

Multiply $y$ by $y$ .

$y^{2} + 6 \cdot - 6 = 45$

Step 2.2.2.2

Multiply $6$ by $- 6$ .

$y^{2} - 36 = 45$

Step 3

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

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Step 3.1

Add $36$ to both sides of the equation.

$y^{2} = 45 + 36$

Step 3.2

Add $45$ and $36$ .

$y^{2} = 81$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{81}$

Step 5

Simplify $\pm \sqrt{81}$ .

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Step 5.1

Rewrite $81$ as $9^{2}$ .

$y = \pm \sqrt{9^{2}}$

Step 5.2

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 9$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

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Step 6.1

First, use the positive value of the $\pm$ to find the first solution.

$y = 9$

Step 6.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 9$

Step 6.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = 9, - 9$