Basic Math Examples

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

Step 1

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

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Apply the distributive property.

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

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 $a$ by $a$ .

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

Step 1.2.1.2

Move $3$ to the left of $a$ .

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

Step 1.2.1.3

Multiply $2$ by $3$ .

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

Step 1.2.2

Add $3 a$ and $2 a$ .

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

Step 1.3

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

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

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 $a^{2}$ by $a$ by adding the exponents.

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Step 1.4.1.1.1

Multiply $a^{2}$ by $a$ .

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Step 1.4.1.1.1.1

Raise $a$ to the power of $1$ .

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

Step 1.4.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.4.1.1.2

Add $2$ and $1$ .

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

Step 1.4.1.2

Move $- 5$ to the left of $a^{2}$ .

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

Step 1.4.1.3

Multiply $a$ by $a$ by adding the exponents.

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Step 1.4.1.3.1

Move $a$ .

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

Step 1.4.1.3.2

Multiply $a$ by $a$ .

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

Step 1.4.1.4

Multiply $- 5$ by $5$ .

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

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