Solve for d (3d+3)/4-2=(12d-3)/10

$\frac{3 d + 3}{4} - 2 = \frac{12 d - 3}{10}$

Multiply both sides by $10$ .

$(\frac{3 d + 3}{4} - 2) \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Simplify.

Simplify the left side.

Simplify $(\frac{3 d + 3}{4} - 2) \cdot 10$ .

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

Factor $3$ out of $3 d$ .

$(\frac{3 (d) + 3}{4} - 2) \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Factor $3$ out of $3$ .

$(\frac{3 (d) + 3 (1)}{4} - 2) \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Factor $3$ out of $3 (d) + 3 (1)$ .

$(\frac{3 (d + 1)}{4} - 2) \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{3 (d + 1)}{4} - 2 \cdot \frac{4}{4}) \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Simplify terms.

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

$(\frac{3 (d + 1)}{4} + \frac{- 2 \cdot 4}{4}) \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Combine the numerators over the common denominator.

$\frac{3 (d + 1) - 2 \cdot 4}{4} \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Simplify the numerator.

Apply the distributive property.

$\frac{3 d + 3 \cdot 1 - 2 \cdot 4}{4} \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Multiply $3$ by $1$ .

$\frac{3 d + 3 - 2 \cdot 4}{4} \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Multiply $- 2$ by $4$ .

$\frac{3 d + 3 - 8}{4} \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Subtract $8$ from $3$ .

$\frac{3 d - 5}{4} \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3 d - 5}{2 (2)} \cdot 10 = \frac{12 d - 3}{10} \cdot 10$

Factor $2$ out of $10$ .

$\frac{3 d - 5}{2 \cdot 2} \cdot (2 \cdot 5) = \frac{12 d - 3}{10} \cdot 10$

Cancel the common factor.

$\frac{3 d - 5}{2 \cdot 2} \cdot (2 \cdot 5) = \frac{12 d - 3}{10} \cdot 10$

Rewrite the expression.

$\frac{3 d - 5}{2} \cdot 5 = \frac{12 d - 3}{10} \cdot 10$

Combine $\frac{3 d - 5}{2}$ and $5$ .

$\frac{(3 d - 5) \cdot 5}{2} = \frac{12 d - 3}{10} \cdot 10$

Move $5$ to the left of $3 d - 5$ .

$\frac{5 (3 d - 5)}{2} = \frac{12 d - 3}{10} \cdot 10$

Simplify the right side.

Simplify $\frac{12 d - 3}{10} \cdot 10$ .

Factor $3$ out of $12 d - 3$ .

Factor $3$ out of $12 d$ .

$\frac{5 (3 d - 5)}{2} = \frac{3 (4 d) - 3}{10} \cdot 10$

Factor $3$ out of $- 3$ .

$\frac{5 (3 d - 5)}{2} = \frac{3 (4 d) + 3 (- 1)}{10} \cdot 10$

Factor $3$ out of $3 (4 d) + 3 (- 1)$ .

$\frac{5 (3 d - 5)}{2} = \frac{3 (4 d - 1)}{10} \cdot 10$

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{5 (3 d - 5)}{2} = \frac{3 (4 d - 1)}{10} \cdot 10$

Rewrite the expression.

$\frac{5 (3 d - 5)}{2} = 3 (4 d - 1)$

Apply the distributive property.

$\frac{5 (3 d - 5)}{2} = 3 (4 d) + 3 \cdot - 1$

Multiply.

Multiply $4$ by $3$ .

$\frac{5 (3 d - 5)}{2} = 12 d + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$\frac{5 (3 d - 5)}{2} = 12 d - 3$

Solve for $d$ .

Multiply both sides by $2$ .

$\frac{5 (3 d - 5)}{2} \cdot 2 = (12 d - 3) \cdot 2$

Simplify.

Simplify the left side.

Simplify $\frac{5 (3 d - 5)}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 (3 d - 5)}{2} \cdot 2 = (12 d - 3) \cdot 2$

Rewrite the expression.

$5 (3 d - 5) = (12 d - 3) \cdot 2$

Apply the distributive property.

$5 (3 d) + 5 \cdot - 5 = (12 d - 3) \cdot 2$

Multiply.

Multiply $3$ by $5$ .

$15 d + 5 \cdot - 5 = (12 d - 3) \cdot 2$

Multiply $5$ by $- 5$ .

$15 d - 25 = (12 d - 3) \cdot 2$

Simplify the right side.

Simplify $(12 d - 3) \cdot 2$ .

Apply the distributive property.

$15 d - 25 = 12 d \cdot 2 - 3 \cdot 2$

Multiply.

Multiply $2$ by $12$ .

$15 d - 25 = 24 d - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$15 d - 25 = 24 d - 6$

Solve for $d$ .

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

Subtract $24 d$ from both sides of the equation.

$15 d - 25 - 24 d = - 6$

Subtract $24 d$ from $15 d$ .

$- 9 d - 25 = - 6$

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

Add $25$ to both sides of the equation.

$- 9 d = - 6 + 25$

Add $- 6$ and $25$ .

$- 9 d = 19$

Divide each term in $- 9 d = 19$ by $- 9$ and simplify.

Divide each term in $- 9 d = 19$ by $- 9$ .

$\frac{- 9 d}{- 9} = \frac{19}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 d}{- 9} = \frac{19}{- 9}$

Divide $d$ by $1$ .

$d = \frac{19}{- 9}$

Simplify the right side.

Move the negative in front of the fraction.

$d = - \frac{19}{9}$

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{19}{9}$

Decimal Form:

$d = - 2.\overline{1}$

Mixed Number Form:

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

Solve for d (3d+3)/4-2=(12d-3)/10

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