Basic Math Examples

$\frac{3}{2} \cdot (d + 8) = 6 d$

Step 1

Simplify $\frac{3}{2} \cdot (d + 8)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{3}{2} \cdot (d + 8) = 6 d$

Step 1.2

Simplify by adding zeros.

$\frac{3}{2} \cdot (d + 8) = 6 d$

Step 1.3

Apply the distributive property.

$\frac{3}{2} d + \frac{3}{2} \cdot 8 = 6 d$

Step 1.4

Combine $\frac{3}{2}$ and $d$ .

$\frac{3 d}{2} + \frac{3}{2} \cdot 8 = 6 d$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $8$ .

$\frac{3 d}{2} + \frac{3}{2} \cdot (2 (4)) = 6 d$

Step 1.5.2

Cancel the common factor.

$\frac{3 d}{2} + \frac{3}{2} \cdot (2 \cdot 4) = 6 d$

Step 1.5.3

Rewrite the expression.

$\frac{3 d}{2} + 3 \cdot 4 = 6 d$

Step 1.6

Multiply $3$ by $4$ .

$\frac{3 d}{2} + 12 = 6 d$

Step 2

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

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Step 2.1

Subtract $6 d$ from both sides of the equation.

$\frac{3 d}{2} + 12 - 6 d = 0$

Step 2.2

To write $- 6 d$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 d}{2} - 6 d \cdot \frac{2}{2} + 12 = 0$

Step 2.3

Combine $- 6 d$ and $\frac{2}{2}$ .

$\frac{3 d}{2} + \frac{- 6 d \cdot 2}{2} + 12 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 d - 6 d \cdot 2}{2} + 12 = 0$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $3 d$ out of $3 d - 6 d \cdot 2$ .

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Step 2.5.1.1.1

Factor $3 d$ out of $3 d$ .

$\frac{3 d (1) - 6 d \cdot 2}{2} + 12 = 0$

Step 2.5.1.1.2

Factor $3 d$ out of $- 6 d \cdot 2$ .

$\frac{3 d (1) + 3 d (- 2 \cdot 2)}{2} + 12 = 0$

Step 2.5.1.1.3

Factor $3 d$ out of $3 d (1) + 3 d (- 2 \cdot 2)$ .

$\frac{3 d (1 - 2 \cdot 2)}{2} + 12 = 0$

Step 2.5.1.2

Multiply $- 2$ by $2$ .

$\frac{3 d (1 - 4)}{2} + 12 = 0$

Step 2.5.1.3

Subtract $4$ from $1$ .

$\frac{3 d \cdot - 3}{2} + 12 = 0$

Step 2.5.1.4

Multiply $- 3$ by $3$ .

$\frac{- 9 d}{2} + 12 = 0$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{9 d}{2} + 12 = 0$

Step 3

Subtract $12$ from both sides of the equation.

$- \frac{9 d}{2} = - 12$

Step 4

Multiply both sides of the equation by $- \frac{2}{9}$ .

$- \frac{2}{9} (- \frac{9 d}{2}) = - \frac{2}{9} \cdot - 12$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{2}{9} (- \frac{9 d}{2})$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{2}{9}$ into the numerator.

$\frac{- 2}{9} (- \frac{9 d}{2}) = - \frac{2}{9} \cdot - 12$

Step 5.1.1.1.2

Move the leading negative in $- \frac{9 d}{2}$ into the numerator.

$\frac{- 2}{9} \cdot \frac{- 9 d}{2} = - \frac{2}{9} \cdot - 12$

Step 5.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{9} \cdot \frac{- 9 d}{2} = - \frac{2}{9} \cdot - 12$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{9} \cdot \frac{- 9 d}{2} = - \frac{2}{9} \cdot - 12$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{9} (- 9 d) = - \frac{2}{9} \cdot - 12$

Step 5.1.1.2

Cancel the common factor of $9$ .

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Step 5.1.1.2.1

Factor $9$ out of $- 9 d$ .

$\frac{- 1}{9} (9 (- d)) = - \frac{2}{9} \cdot - 12$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{9} (9 (- d)) = - \frac{2}{9} \cdot - 12$

Step 5.1.1.2.3

Rewrite the expression.

$- - d = - \frac{2}{9} \cdot - 12$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 d = - \frac{2}{9} \cdot - 12$

Step 5.1.1.3.2

Multiply $d$ by $1$ .

$d = - \frac{2}{9} \cdot - 12$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{2}{9} \cdot - 12$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{2}{9}$ into the numerator.

$d = \frac{- 2}{9} \cdot - 12$

Step 5.2.1.1.2

Factor $3$ out of $9$ .

$d = \frac{- 2}{3 (3)} \cdot - 12$

Step 5.2.1.1.3

Factor $3$ out of $- 12$ .

$d = \frac{- 2}{3 \cdot 3} \cdot (3 \cdot - 4)$

Step 5.2.1.1.4

Cancel the common factor.

$d = \frac{- 2}{3 \cdot 3} \cdot (3 \cdot - 4)$

Step 5.2.1.1.5

Rewrite the expression.

$d = \frac{- 2}{3} \cdot - 4$

Step 5.2.1.2

Combine $\frac{- 2}{3}$ and $- 4$ .

$d = \frac{- 2 \cdot - 4}{3}$

Step 5.2.1.3

Multiply $- 2$ by $- 4$ .

$d = \frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$d = \frac{8}{3}$

Decimal Form:

$d = 2.\overline{6}$

Mixed Number Form:

$d = 2 \frac{2}{3}$