Solve for b -5/6(8+5b)=75+5/3b

$- \frac{5}{6} (8 + 5 b) = 75 + \frac{5}{3} b$

Step 1

Simplify $- \frac{5}{6} \cdot (8 + 5 b)$ .

Rewrite.

$0 + 0 - \frac{5}{6} \cdot (8 + 5 b) = 75 + \frac{5}{3} b$

Simplify by adding zeros.

$- \frac{5}{6} \cdot (8 + 5 b) = 75 + \frac{5}{3} b$

Apply the distributive property.

$- \frac{5}{6} \cdot 8 - \frac{5}{6} (5 b) = 75 + \frac{5}{3} b$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{- 5}{6} \cdot 8 - \frac{5}{6} (5 b) = 75 + \frac{5}{3} b$

Factor $2$ out of $6$ .

$\frac{- 5}{2 (3)} \cdot 8 - \frac{5}{6} (5 b) = 75 + \frac{5}{3} b$

Factor $2$ out of $8$ .

$\frac{- 5}{2 \cdot 3} \cdot (2 \cdot 4) - \frac{5}{6} (5 b) = 75 + \frac{5}{3} b$

Cancel the common factor.

$\frac{- 5}{2 \cdot 3} \cdot (2 \cdot 4) - \frac{5}{6} (5 b) = 75 + \frac{5}{3} b$

Rewrite the expression.

$\frac{- 5}{3} \cdot 4 - \frac{5}{6} (5 b) = 75 + \frac{5}{3} b$

Combine $\frac{- 5}{3}$ and $4$ .

$\frac{- 5 \cdot 4}{3} - \frac{5}{6} (5 b) = 75 + \frac{5}{3} b$

Multiply $- 5$ by $4$ .

$\frac{- 20}{3} - \frac{5}{6} (5 b) = 75 + \frac{5}{3} b$

Multiply $- \frac{5}{6} (5 b)$ .

Multiply $5$ by $- 1$ .

$\frac{- 20}{3} - 5 (\frac{5}{6}) b = 75 + \frac{5}{3} b$

Combine $- 5$ and $\frac{5}{6}$ .

$\frac{- 20}{3} + \frac{- 5 \cdot 5}{6} b = 75 + \frac{5}{3} b$

Multiply $- 5$ by $5$ .

$\frac{- 20}{3} + \frac{- 25}{6} b = 75 + \frac{5}{3} b$

Combine $\frac{- 25}{6}$ and $b$ .

$\frac{- 20}{3} + \frac{- 25 b}{6} = 75 + \frac{5}{3} b$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{20}{3} + \frac{- 25 b}{6} = 75 + \frac{5}{3} b$

Move the negative in front of the fraction.

$- \frac{20}{3} - \frac{25 b}{6} = 75 + \frac{5}{3} b$

Step 2

Combine $\frac{5}{3}$ and $b$ .

$- \frac{20}{3} - \frac{25 b}{6} = 75 + \frac{5 b}{3}$

Step 3

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

Subtract $\frac{5 b}{3}$ from both sides of the equation.

$- \frac{20}{3} - \frac{25 b}{6} - \frac{5 b}{3} = 75$

To write $- \frac{5 b}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{20}{3} - \frac{25 b}{6} - \frac{5 b}{3} \cdot \frac{2}{2} = 75$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 b}{3}$ by $\frac{2}{2}$ .

$- \frac{20}{3} - \frac{25 b}{6} - \frac{5 b \cdot 2}{3 \cdot 2} = 75$

Multiply $3$ by $2$ .

$- \frac{20}{3} - \frac{25 b}{6} - \frac{5 b \cdot 2}{6} = 75$

Combine the numerators over the common denominator.

$- \frac{20}{3} + \frac{- 25 b - 5 b \cdot 2}{6} = 75$

Simplify each term.

Simplify the numerator.

Factor $5 b$ out of $- 25 b - 5 b \cdot 2$ .

Factor $5 b$ out of $- 25 b$ .

$- \frac{20}{3} + \frac{5 b (- 5) - 5 b \cdot 2}{6} = 75$

Factor $5 b$ out of $- 5 b \cdot 2$ .

$- \frac{20}{3} + \frac{5 b (- 5) + 5 b (- 1 \cdot 2)}{6} = 75$

Factor $5 b$ out of $5 b (- 5) + 5 b (- 1 \cdot 2)$ .

$- \frac{20}{3} + \frac{5 b (- 5 - 1 \cdot 2)}{6} = 75$

Multiply $- 1$ by $2$ .

$- \frac{20}{3} + \frac{5 b (- 5 - 2)}{6} = 75$

Subtract $2$ from $- 5$ .

$- \frac{20}{3} + \frac{5 b \cdot - 7}{6} = 75$

Multiply $- 7$ by $5$ .

$- \frac{20}{3} + \frac{- 35 b}{6} = 75$

Move the negative in front of the fraction.

$- \frac{20}{3} - \frac{35 b}{6} = 75$

Step 4

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

Add $\frac{20}{3}$ to both sides of the equation.

$- \frac{35 b}{6} = 75 + \frac{20}{3}$

To write $75$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{35 b}{6} = 75 \cdot \frac{3}{3} + \frac{20}{3}$

Combine $75$ and $\frac{3}{3}$ .

$- \frac{35 b}{6} = \frac{75 \cdot 3}{3} + \frac{20}{3}$

Combine the numerators over the common denominator.

$- \frac{35 b}{6} = \frac{75 \cdot 3 + 20}{3}$

Simplify the numerator.

Multiply $75$ by $3$ .

$- \frac{35 b}{6} = \frac{225 + 20}{3}$

Add $225$ and $20$ .

$- \frac{35 b}{6} = \frac{245}{3}$

Step 5

Multiply both sides of the equation by $- \frac{6}{35}$ .

$- \frac{6}{35} (- \frac{35 b}{6}) = - \frac{6}{35} \cdot \frac{245}{3}$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{35} (- \frac{35 b}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{35}$ into the numerator.

$\frac{- 6}{35} (- \frac{35 b}{6}) = - \frac{6}{35} \cdot \frac{245}{3}$

Move the leading negative in $- \frac{35 b}{6}$ into the numerator.

$\frac{- 6}{35} \cdot \frac{- 35 b}{6} = - \frac{6}{35} \cdot \frac{245}{3}$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{35} \cdot \frac{- 35 b}{6} = - \frac{6}{35} \cdot \frac{245}{3}$

Cancel the common factor.

$\frac{6 \cdot - 1}{35} \cdot \frac{- 35 b}{6} = - \frac{6}{35} \cdot \frac{245}{3}$

Rewrite the expression.

$\frac{- 1}{35} (- 35 b) = - \frac{6}{35} \cdot \frac{245}{3}$

Cancel the common factor of $35$ .

Factor $35$ out of $- 35 b$ .

$\frac{- 1}{35} (35 (- b)) = - \frac{6}{35} \cdot \frac{245}{3}$

Cancel the common factor.

$\frac{- 1}{35} (35 (- b)) = - \frac{6}{35} \cdot \frac{245}{3}$

Rewrite the expression.

$- - b = - \frac{6}{35} \cdot \frac{245}{3}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 b = - \frac{6}{35} \cdot \frac{245}{3}$

Multiply $b$ by $1$ .

$b = - \frac{6}{35} \cdot \frac{245}{3}$

Simplify the right side.

Simplify $- \frac{6}{35} \cdot \frac{245}{3}$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{6}{35}$ into the numerator.

$b = \frac{- 6}{35} \cdot \frac{245}{3}$

Factor $3$ out of $- 6$ .

$b = \frac{3 (- 2)}{35} \cdot \frac{245}{3}$

Cancel the common factor.

$b = \frac{3 \cdot - 2}{35} \cdot \frac{245}{3}$

Rewrite the expression.

$b = \frac{- 2}{35} \cdot 245$

Cancel the common factor of $35$ .

Factor $35$ out of $245$ .

$b = \frac{- 2}{35} \cdot (35 (7))$

Cancel the common factor.

$b = \frac{- 2}{35} \cdot (35 \cdot 7)$

Rewrite the expression.

$b = - 2 \cdot 7$

Multiply $- 2$ by $7$ .

$b = - 14$

Solve for b -5/6(8+5b)=75+5/3b

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