Basic Math Examples

$54 = \frac{1}{2} \cdot (h (2 + b))$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (h (2 + b)) = 54$ .

$\frac{1}{2} \cdot (h (2 + b)) = 54$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (h (2 + b))) = 2 \cdot 54$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $2 (\frac{1}{2} \cdot (h (2 + b)))$ .

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Step 3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} \cdot (h \cdot 2 + h b)) = 2 \cdot 54$

Step 3.1.1.2

Move $2$ to the left of $h$ .

$2 (\frac{1}{2} \cdot (2 \cdot h + h b)) = 2 \cdot 54$

Step 3.1.1.3

Apply the distributive property.

$2 (\frac{1}{2} (2 h) + \frac{1}{2} (h b)) = 2 \cdot 54$

Step 3.1.1.4

Cancel the common factor of $2$ .

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Step 3.1.1.4.1

Factor $2$ out of $2 h$ .

$2 (\frac{1}{2} (2 (h)) + \frac{1}{2} (h b)) = 2 \cdot 54$

Step 3.1.1.4.2

Cancel the common factor.

$2 (\frac{1}{2} (2 h) + \frac{1}{2} (h b)) = 2 \cdot 54$

Step 3.1.1.4.3

Rewrite the expression.

$2 (h + \frac{1}{2} (h b)) = 2 \cdot 54$

Step 3.1.1.5

Multiply $\frac{1}{2} (h b)$ .

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Step 3.1.1.5.1

Combine $h$ and $\frac{1}{2}$ .

$2 (h + \frac{h}{2} b) = 2 \cdot 54$

Step 3.1.1.5.2

Combine $\frac{h}{2}$ and $b$ .

$2 (h + \frac{h b}{2}) = 2 \cdot 54$

Step 3.1.1.6

Apply the distributive property.

$2 h + 2 \frac{h b}{2} = 2 \cdot 54$

Step 3.1.1.7

Cancel the common factor of $2$ .

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Step 3.1.1.7.1

Cancel the common factor.

$2 h + 2 \frac{h b}{2} = 2 \cdot 54$

Step 3.1.1.7.2

Rewrite the expression.

$2 h + h b = 2 \cdot 54$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $54$ .

$2 h + h b = 108$

Step 4

Factor $h$ out of $2 h + h b$ .

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Step 4.1

Factor $h$ out of $2 h$ .

$h \cdot 2 + h b = 108$

Step 4.2

Factor $h$ out of $h b$ .

$h \cdot 2 + h (b) = 108$

Step 4.3

Factor $h$ out of $h \cdot 2 + h (b)$ .

$h (2 + b) = 108$

Step 5

Divide each term in $h (2 + b) = 108$ by $2 + b$ and simplify.

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Step 5.1

Divide each term in $h (2 + b) = 108$ by $2 + b$ .

$\frac{h (2 + b)}{2 + b} = \frac{108}{2 + b}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2 + b$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{h (2 + b)}{2 + b} = \frac{108}{2 + b}$

Step 5.2.1.2

Divide $h$ by $1$ .

$h = \frac{108}{2 + b}$