Basic Math Examples

(a + 2) (a + 3) (a - 5) = 44

$(a + 2) (a + 3) (a - 5) = 44$

Step 1

Simplify

(a + 2) (a + 3) (a - 5)

$(a + 2) (a + 3) (a - 5)$ .

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Step 1.1

Expand

(a + 2) (a + 3)

$(a + 2) (a + 3)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

(a (a + 3) + 2 (a + 3)) (a - 5) = 44

$(a (a + 3) + 2 (a + 3)) (a - 5) = 44$

Step 1.1.2

Apply the distributive property.

(a \cdot a + a \cdot 3 + 2 (a + 3)) (a - 5) = 44

$(a \cdot a + a \cdot 3 + 2 (a + 3)) (a - 5) = 44$

Step 1.1.3

Apply the distributive property.

(a \cdot a + a \cdot 3 + 2 a + 2 \cdot 3) (a - 5) = 44

$(a \cdot a + a \cdot 3 + 2 a + 2 \cdot 3) (a - 5) = 44$

(a \cdot a + a \cdot 3 + 2 a + 2 \cdot 3) (a - 5) = 44

$(a \cdot a + a \cdot 3 + 2 a + 2 \cdot 3) (a - 5) = 44$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply

a

$a$ by

a

$a$ .

(a^{2} + a \cdot 3 + 2 a + 2 \cdot 3) (a - 5) = 44

$(a^{2} + a \cdot 3 + 2 a + 2 \cdot 3) (a - 5) = 44$

Step 1.2.1.2

Move

3

$3$ to the left of

a

$a$ .

(a^{2} + 3 \cdot a + 2 a + 2 \cdot 3) (a - 5) = 44

$(a^{2} + 3 \cdot a + 2 a + 2 \cdot 3) (a - 5) = 44$

Step 1.2.1.3

Multiply

2

$2$ by

3

$3$ .

(a^{2} + 3 a + 2 a + 6) (a - 5) = 44

$(a^{2} + 3 a + 2 a + 6) (a - 5) = 44$

(a^{2} + 3 a + 2 a + 6) (a - 5) = 44

$(a^{2} + 3 a + 2 a + 6) (a - 5) = 44$

Step 1.2.2

Add

3 a

$3 a$ and

2 a

$2 a$ .

(a^{2} + 5 a + 6) (a - 5) = 44

$(a^{2} + 5 a + 6) (a - 5) = 44$

(a^{2} + 5 a + 6) (a - 5) = 44

$(a^{2} + 5 a + 6) (a - 5) = 44$

Step 1.3

Expand

(a^{2} + 5 a + 6) (a - 5)

$(a^{2} + 5 a + 6) (a - 5)$ by multiplying each term in the first expression by each term in the second expression.

a^{2} a + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{2} a + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

Step 1.4

Simplify terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply

a^{2}

$a^{2}$ by

a

$a$ by adding the exponents.

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Step 1.4.1.1.1

Multiply

a^{2}

$a^{2}$ by

a

$a$ .

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Step 1.4.1.1.1.1

Raise

a

$a$ to the power of

1

$1$ .

a^{2} a^{1} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{2} a^{1} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

Step 1.4.1.1.1.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

a^{2 + 1} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{2 + 1} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

a^{2 + 1} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{2 + 1} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

Step 1.4.1.1.2

Add

2

$2$ and

1

$1$ .

a^{3} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{3} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

a^{3} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{3} + a^{2} \cdot - 5 + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

Step 1.4.1.2

Move

- 5

$- 5$ to the left of

a^{2}

$a^{2}$ .

a^{3} - 5 \cdot a^{2} + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{3} - 5 \cdot a^{2} + 5 a \cdot a + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

Step 1.4.1.3

Multiply

a

$a$ by

a

$a$ by adding the exponents.

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Step 1.4.1.3.1

Move

a

$a$ .

a^{3} - 5 a^{2} + 5 (a \cdot a) + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{3} - 5 a^{2} + 5 (a \cdot a) + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

Step 1.4.1.3.2

Multiply

a

$a$ by

a

$a$ .

a^{3} - 5 a^{2} + 5 a^{2} + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{3} - 5 a^{2} + 5 a^{2} + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

a^{3} - 5 a^{2} + 5 a^{2} + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44

$a^{3} - 5 a^{2} + 5 a^{2} + 5 a \cdot - 5 + 6 a + 6 \cdot - 5 = 44$

Step 1.4.1.4

Multiply

- 5

$- 5$ by

5

$5$ .

a^{3} - 5 a^{2} + 5 a^{2} - 25 a + 6 a + 6 \cdot - 5 = 44

$a^{3} - 5 a^{2} + 5 a^{2} - 25 a + 6 a + 6 \cdot - 5 = 44$

Step 1.4.1.5

Multiply

$6$ by

$- 5$ .

$a^{3} - 5 a^{2} + 5 a^{2} - 25 a + 6 a - 30 = 44$

Step 1.4.2

Simplify by adding terms.

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Step 1.4.2.1

Combine the opposite terms in

$a^{3} - 5 a^{2} + 5 a^{2} - 25 a + 6 a - 30$ .

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Step 1.4.2.1.1

Add

$- 5 a^{2}$ and

$5 a^{2}$ .

$a^{3} + 0 - 25 a + 6 a - 30 = 44$

Step 1.4.2.1.2

Add

$a^{3}$ and

$0$ .

$a^{3} - 25 a + 6 a - 30 = 44$

Step 1.4.2.2

Add

$- 25 a$ and

$6 a$ .

$a^{3} - 19 a - 30 = 44$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$a \approx 5.66283201$

Step 3