Basic Math Examples

$\frac{2 r + 12}{8} = \frac{3 r - 36}{3}$

Step 1

Cancel the common factor of $2 r + 12$ and $8$ .

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Step 1.1

Factor $2$ out of $2 r$ .

$\frac{2 (r) + 12}{8} = \frac{3 r - 36}{3}$

Step 1.2

Factor $2$ out of $12$ .

$\frac{2 r + 2 \cdot 6}{8} = \frac{3 r - 36}{3}$

Step 1.3

Factor $2$ out of $2 r + 2 \cdot 6$ .

$\frac{2 (r + 6)}{8} = \frac{3 r - 36}{3}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $8$ .

$\frac{2 (r + 6)}{2 (4)} = \frac{3 r - 36}{3}$

Step 1.4.2

Cancel the common factor.

$\frac{2 (r + 6)}{2 \cdot 4} = \frac{3 r - 36}{3}$

Step 1.4.3

Rewrite the expression.

$\frac{r + 6}{4} = \frac{3 r - 36}{3}$

Step 2

Multiply both sides by $4$ .

$\frac{r + 6}{4} \cdot 4 = \frac{3 r - 36}{3} \cdot 4$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{r + 6}{4} \cdot 4 = \frac{3 r - 36}{3} \cdot 4$

Step 3.1.1.2

Rewrite the expression.

$r + 6 = \frac{3 r - 36}{3} \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{3 r - 36}{3} \cdot 4$ .

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Step 3.2.1.1

Factor $3$ out of $3 r - 36$ .

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Step 3.2.1.1.1

Factor $3$ out of $3 r$ .

$r + 6 = \frac{3 (r) - 36}{3} \cdot 4$

Step 3.2.1.1.2

Factor $3$ out of $- 36$ .

$r + 6 = \frac{3 r + 3 \cdot - 12}{3} \cdot 4$

Step 3.2.1.1.3

Factor $3$ out of $3 r + 3 \cdot - 12$ .

$r + 6 = \frac{3 (r - 12)}{3} \cdot 4$

Step 3.2.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.2.1

Cancel the common factor.

$r + 6 = \frac{3 (r - 12)}{3} \cdot 4$

Step 3.2.1.2.2

Divide $r - 12$ by $1$ .

$r + 6 = (r - 12) \cdot 4$

Step 3.2.1.3

Apply the distributive property.

$r + 6 = r \cdot 4 - 12 \cdot 4$

Step 3.2.1.4

Simplify the expression.

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Step 3.2.1.4.1

Move $4$ to the left of $r$ .

$r + 6 = 4 \cdot r - 12 \cdot 4$

Step 3.2.1.4.2

Multiply $- 12$ by $4$ .

$r + 6 = 4 r - 48$

Step 4

Solve for $r$ .

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Step 4.1

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

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Step 4.1.1

Subtract $4 r$ from both sides of the equation.

$r + 6 - 4 r = - 48$

Step 4.1.2

Subtract $4 r$ from $r$ .

$- 3 r + 6 = - 48$

Step 4.2

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

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Step 4.2.1

Subtract $6$ from both sides of the equation.

$- 3 r = - 48 - 6$

Step 4.2.2

Subtract $6$ from $- 48$ .

$- 3 r = - 54$

Step 4.3

Divide each term in $- 3 r = - 54$ by $- 3$ and simplify.

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Step 4.3.1

Divide each term in $- 3 r = - 54$ by $- 3$ .

$\frac{- 3 r}{- 3} = \frac{- 54}{- 3}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 3$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 3 r}{- 3} = \frac{- 54}{- 3}$

Step 4.3.2.1.2

Divide $r$ by $1$ .

$r = \frac{- 54}{- 3}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 54$ by $- 3$ .

$r = 18$