Basic Math Examples

$c = \frac{7 d - 6}{3 + 8 d}$

Step 1

Rewrite the equation as $\frac{7 d - 6}{3 + 8 d} = c$ .

$\frac{7 d - 6}{3 + 8 d} = c$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 + 8 d, 1$

Step 2.2

Remove parentheses.

$3 + 8 d, 1$

Step 2.3

The LCM of one and any expression is the expression.

$3 + 8 d$

Step 3

Multiply each term in $\frac{7 d - 6}{3 + 8 d} = c$ by $3 + 8 d$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{7 d - 6}{3 + 8 d} = c$ by $3 + 8 d$ .

$\frac{7 d - 6}{3 + 8 d} (3 + 8 d) = c (3 + 8 d)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3 + 8 d$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 d - 6}{3 + 8 d} (3 + 8 d) = c (3 + 8 d)$

Step 3.2.1.2

Rewrite the expression.

$7 d - 6 = c (3 + 8 d)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$7 d - 6 = c \cdot 3 + c (8 d)$

Step 3.3.2

Reorder.

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Step 3.3.2.1

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

$7 d - 6 = 3 \cdot c + c (8 d)$

Step 3.3.2.2

Rewrite using the commutative property of multiplication.

$7 d - 6 = 3 c + 8 c d$

Step 4

Solve the equation.

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Step 4.1

Subtract $8 c d$ from both sides of the equation.

$7 d - 6 - 8 c d = 3 c$

Step 4.2

Add $6$ to both sides of the equation.

$7 d - 8 c d = 3 c + 6$

Step 4.3

Factor $d$ out of $7 d - 8 c d$ .

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Step 4.3.1

Factor $d$ out of $7 d$ .

$d \cdot 7 - 8 c d = 3 c + 6$

Step 4.3.2

Factor $d$ out of $- 8 c d$ .

$d \cdot 7 + d (- 8 c) = 3 c + 6$

Step 4.3.3

Factor $d$ out of $d \cdot 7 + d (- 8 c)$ .

$d (7 - 8 c) = 3 c + 6$

Step 4.4

Divide each term in $d (7 - 8 c) = 3 c + 6$ by $7 - 8 c$ and simplify.

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Step 4.4.1

Divide each term in $d (7 - 8 c) = 3 c + 6$ by $7 - 8 c$ .

$\frac{d (7 - 8 c)}{7 - 8 c} = \frac{3 c}{7 - 8 c} + \frac{6}{7 - 8 c}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $7 - 8 c$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{d (7 - 8 c)}{7 - 8 c} = \frac{3 c}{7 - 8 c} + \frac{6}{7 - 8 c}$

Step 4.4.2.1.2

Divide $d$ by $1$ .

$d = \frac{3 c}{7 - 8 c} + \frac{6}{7 - 8 c}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Combine the numerators over the common denominator.

$d = \frac{3 c + 6}{7 - 8 c}$

Step 4.4.3.2

Factor $3$ out of $3 c + 6$ .

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Step 4.4.3.2.1

Factor $3$ out of $3 c$ .

$d = \frac{3 (c) + 6}{7 - 8 c}$

Step 4.4.3.2.2

Factor $3$ out of $6$ .

$d = \frac{3 c + 3 \cdot 2}{7 - 8 c}$

Step 4.4.3.2.3

Factor $3$ out of $3 c + 3 \cdot 2$ .

$d = \frac{3 (c + 2)}{7 - 8 c}$