Solve for d 3/5(15d+20)-1/6(18d-12)=38

$\frac{3}{5} (15 d + 20) - \frac{1}{6} (18 d - 12) = 38$

Simplify $\frac{3}{5} \cdot (15 d + 20) - \frac{1}{6} \cdot (18 d - 12)$ .

Simplify each term.

Apply the distributive property.

$\frac{3}{5} (15 d) + \frac{3}{5} \cdot 20 - \frac{1}{6} \cdot (18 d - 12) = 38$

Cancel the common factor of $5$ .

Factor $5$ out of $15 d$ .

$\frac{3}{5} (5 (3 d)) + \frac{3}{5} \cdot 20 - \frac{1}{6} \cdot (18 d - 12) = 38$

Cancel the common factor.

$\frac{3}{5} (5 (3 d)) + \frac{3}{5} \cdot 20 - \frac{1}{6} \cdot (18 d - 12) = 38$

Rewrite the expression.

$3 (3 d) + \frac{3}{5} \cdot 20 - \frac{1}{6} \cdot (18 d - 12) = 38$

Multiply $3$ by $3$ .

$9 d + \frac{3}{5} \cdot 20 - \frac{1}{6} \cdot (18 d - 12) = 38$

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$9 d + \frac{3}{5} \cdot (5 (4)) - \frac{1}{6} \cdot (18 d - 12) = 38$

Cancel the common factor.

$9 d + \frac{3}{5} \cdot (5 \cdot 4) - \frac{1}{6} \cdot (18 d - 12) = 38$

Rewrite the expression.

$9 d + 3 \cdot 4 - \frac{1}{6} \cdot (18 d - 12) = 38$

Multiply $3$ by $4$ .

$9 d + 12 - \frac{1}{6} \cdot (18 d - 12) = 38$

Apply the distributive property.

$9 d + 12 - \frac{1}{6} (18 d) - \frac{1}{6} \cdot - 12 = 38$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$9 d + 12 + \frac{- 1}{6} (18 d) - \frac{1}{6} \cdot - 12 = 38$

Factor $6$ out of $18 d$ .

$9 d + 12 + \frac{- 1}{6} (6 (3 d)) - \frac{1}{6} \cdot - 12 = 38$

Cancel the common factor.

$9 d + 12 + \frac{- 1}{6} (6 (3 d)) - \frac{1}{6} \cdot - 12 = 38$

Rewrite the expression.

$9 d + 12 - 1 (3 d) - \frac{1}{6} \cdot - 12 = 38$

Multiply $3$ by $- 1$ .

$9 d + 12 - 3 d - \frac{1}{6} \cdot - 12 = 38$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$9 d + 12 - 3 d + \frac{- 1}{6} \cdot - 12 = 38$

Factor $6$ out of $- 12$ .

$9 d + 12 - 3 d + \frac{- 1}{6} \cdot (6 (- 2)) = 38$

Cancel the common factor.

$9 d + 12 - 3 d + \frac{- 1}{6} \cdot (6 \cdot - 2) = 38$

Rewrite the expression.

$9 d + 12 - 3 d - 1 \cdot - 2 = 38$

Multiply $- 1$ by $- 2$ .

$9 d + 12 - 3 d + 2 = 38$

Simplify by adding terms.

Subtract $3 d$ from $9 d$ .

$6 d + 12 + 2 = 38$

Add $12$ and $2$ .

$6 d + 14 = 38$

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

Subtract $14$ from both sides of the equation.

$6 d = 38 - 14$

Subtract $14$ from $38$ .

$6 d = 24$

Divide each term in $6 d = 24$ by $6$ and simplify.

Divide each term in $6 d = 24$ by $6$ .

$\frac{6 d}{6} = \frac{24}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 d}{6} = \frac{24}{6}$

Divide $d$ by $1$ .

$d = \frac{24}{6}$

Simplify the right side.

Divide $24$ by $6$ .

$d = 4$

Solve for d 3/5(15d+20)-1/6(18d-12)=38

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