Solve for d 2/3(6+d)-2d=-3/4(d-8)

$\frac{2}{3} (6 + d) - 2 d = - \frac{3}{4} (d - 8)$

Simplify $\frac{2}{3} \cdot (6 + d) - 2 d$ .

Simplify each term.

Apply the distributive property.

$\frac{2}{3} \cdot 6 + \frac{2}{3} d - 2 d = - \frac{3}{4} \cdot (d - 8)$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{2}{3} \cdot (3 (2)) + \frac{2}{3} d - 2 d = - \frac{3}{4} \cdot (d - 8)$

Cancel the common factor.

$\frac{2}{3} \cdot (3 \cdot 2) + \frac{2}{3} d - 2 d = - \frac{3}{4} \cdot (d - 8)$

Rewrite the expression.

$2 \cdot 2 + \frac{2}{3} d - 2 d = - \frac{3}{4} \cdot (d - 8)$

Multiply $2$ by $2$ .

$4 + \frac{2}{3} d - 2 d = - \frac{3}{4} \cdot (d - 8)$

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

$4 + \frac{2 d}{3} - 2 d = - \frac{3}{4} \cdot (d - 8)$

To write $- 2 d$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 + \frac{2 d}{3} - 2 d \cdot \frac{3}{3} = - \frac{3}{4} \cdot (d - 8)$

Simplify terms.

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

$4 + \frac{2 d}{3} + \frac{- 2 d \cdot 3}{3} = - \frac{3}{4} \cdot (d - 8)$

Combine the numerators over the common denominator.

$4 + \frac{2 d - 2 d \cdot 3}{3} = - \frac{3}{4} \cdot (d - 8)$

Simplify each term.

Simplify the numerator.

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

Factor $2 d$ out of $2 d$ .

$4 + \frac{2 d (1) - 2 d \cdot 3}{3} = - \frac{3}{4} \cdot (d - 8)$

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

$4 + \frac{2 d (1) + 2 d (- 1 \cdot 3)}{3} = - \frac{3}{4} \cdot (d - 8)$

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

$4 + \frac{2 d (1 - 1 \cdot 3)}{3} = - \frac{3}{4} \cdot (d - 8)$

Multiply $- 1$ by $3$ .

$4 + \frac{2 d (1 - 3)}{3} = - \frac{3}{4} \cdot (d - 8)$

Subtract $3$ from $1$ .

$4 + \frac{2 d \cdot - 2}{3} = - \frac{3}{4} \cdot (d - 8)$

Multiply $- 2$ by $2$ .

$4 + \frac{- 4 d}{3} = - \frac{3}{4} \cdot (d - 8)$

Move the negative in front of the fraction.

$4 - \frac{4 d}{3} = - \frac{3}{4} \cdot (d - 8)$

Simplify $- \frac{3}{4} \cdot (d - 8)$ .

Simplify terms.

Apply the distributive property.

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

Combine $d$ and $\frac{3}{4}$ .

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

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

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

Factor $4$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 3$ by $- 2$ .

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

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

$4 - \frac{4 d}{3} = - \frac{3 d}{4} + 6$

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

Add $\frac{3 d}{4}$ to both sides of the equation.

$4 - \frac{4 d}{3} + \frac{3 d}{4} = 6$

To write $- \frac{4 d}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

To write $\frac{3 d}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 d}{3}$ by $\frac{4}{4}$ .

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

Multiply $3$ by $4$ .

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

Multiply $\frac{3 d}{4}$ by $\frac{3}{3}$ .

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

Multiply $4$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $d$ out of $- 4 d \cdot 4 + 3 d \cdot 3$ .

Factor $d$ out of $- 4 d \cdot 4$ .

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

Factor $d$ out of $3 d \cdot 3$ .

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

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

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

Multiply $- 4$ by $4$ .

$4 + \frac{d (- 16 + 3 \cdot 3)}{12} = 6$

Multiply $3$ by $3$ .

$4 + \frac{d (- 16 + 9)}{12} = 6$

Add $- 16$ and $9$ .

$4 + \frac{d \cdot - 7}{12} = 6$

Move $- 7$ to the left of $d$ .

$4 + \frac{- 7 \cdot d}{12} = 6$

Move the negative in front of the fraction.

$4 - \frac{7 d}{12} = 6$

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

Subtract $4$ from both sides of the equation.

$- \frac{7 d}{12} = 6 - 4$

Subtract $4$ from $6$ .

$- \frac{7 d}{12} = 2$

Multiply both sides of the equation by $- \frac{12}{7}$ .

$- \frac{12}{7} (- \frac{7 d}{12}) = - \frac{12}{7} \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{12}{7} (- \frac{7 d}{12})$ .

Cancel the common factor of $12$ .

Move the leading negative in $- \frac{12}{7}$ into the numerator.

$\frac{- 12}{7} (- \frac{7 d}{12}) = - \frac{12}{7} \cdot 2$

Move the leading negative in $- \frac{7 d}{12}$ into the numerator.

$\frac{- 12}{7} \cdot \frac{- 7 d}{12} = - \frac{12}{7} \cdot 2$

Factor $12$ out of $- 12$ .

$\frac{12 (- 1)}{7} \cdot \frac{- 7 d}{12} = - \frac{12}{7} \cdot 2$

Cancel the common factor.

$\frac{12 \cdot - 1}{7} \cdot \frac{- 7 d}{12} = - \frac{12}{7} \cdot 2$

Rewrite the expression.

$\frac{- 1}{7} (- 7 d) = - \frac{12}{7} \cdot 2$

Cancel the common factor of $7$ .

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

$\frac{- 1}{7} (7 (- d)) = - \frac{12}{7} \cdot 2$

Cancel the common factor.

$\frac{- 1}{7} (7 (- d)) = - \frac{12}{7} \cdot 2$

Rewrite the expression.

$- - d = - \frac{12}{7} \cdot 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 d = - \frac{12}{7} \cdot 2$

Multiply $d$ by $1$ .

$d = - \frac{12}{7} \cdot 2$

Simplify the right side.

Simplify $- \frac{12}{7} \cdot 2$ .

Multiply $- \frac{12}{7} \cdot 2$ .

Multiply $2$ by $- 1$ .

$d = - 2 (\frac{12}{7})$

Combine $- 2$ and $\frac{12}{7}$ .

$d = \frac{- 2 \cdot 12}{7}$

Multiply $- 2$ by $12$ .

$d = \frac{- 24}{7}$

Move the negative in front of the fraction.

$d = - \frac{24}{7}$

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{24}{7}$

Decimal Form:

$d = - 3.\overline{428571}$

Mixed Number Form:

$d = - 3 \frac{3}{7}$

Solve for d 2/3(6+d)-2d=-3/4(d-8)

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