1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$2 \frac { 1 } { 8 } \cdot ( \frac { 6 } { 7 } m - 3 ) - 1 \frac { 2 } { 3 } \cdot ( \frac { 9 } { 5 } m - 6 )$$

Evaluate

$-\frac{33m}{28}+\frac{29}{8}$

Solution Steps

Multiply $2$ and $8$ to get $16$.

$$\frac{16+1}{8}\left(\frac{6}{7}m-3\right)-\frac{1\times 3+2}{3}\left(\frac{9}{5}m-6\right)$$

Add $16$ and $1$ to get $17$.

$$\frac{17}{8}\left(\frac{6}{7}m-3\right)-\frac{1\times 3+2}{3}\left(\frac{9}{5}m-6\right)$$

Use the distributive property to multiply $\frac{17}{8}$ by $\frac{6}{7}m-3$.

$$\frac{17}{8}\times \frac{6}{7}m+\frac{17}{8}\left(-3\right)-\frac{1\times 3+2}{3}\left(\frac{9}{5}m-6\right)$$

Multiply $\frac{17}{8}$ times $\frac{6}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 6}{8\times 7}m+\frac{17}{8}\left(-3\right)-\frac{1\times 3+2}{3}\left(\frac{9}{5}m-6\right)$$

Do the multiplications in the fraction $\frac{17\times 6}{8\times 7}$.

$$\frac{102}{56}m+\frac{17}{8}\left(-3\right)-\frac{1\times 3+2}{3}\left(\frac{9}{5}m-6\right)$$

Reduce the fraction $\frac{102}{56}$ to lowest terms by extracting and canceling out $2$.

$$\frac{51}{28}m+\frac{17}{8}\left(-3\right)-\frac{1\times 3+2}{3}\left(\frac{9}{5}m-6\right)$$

Express $\frac{17}{8}\left(-3\right)$ as a single fraction.

$$\frac{51}{28}m+\frac{17\left(-3\right)}{8}-\frac{1\times 3+2}{3}\left(\frac{9}{5}m-6\right)$$

Multiply $17$ and $-3$ to get $-51$.

$$\frac{51}{28}m+\frac{-51}{8}-\frac{1\times 3+2}{3}\left(\frac{9}{5}m-6\right)$$

Fraction $\frac{-51}{8}$ can be rewritten as $-\frac{51}{8}$ by extracting the negative sign.

$$\frac{51}{28}m-\frac{51}{8}-\frac{1\times 3+2}{3}\left(\frac{9}{5}m-6\right)$$

Multiply $1$ and $3$ to get $3$.

$$\frac{51}{28}m-\frac{51}{8}-\frac{3+2}{3}\left(\frac{9}{5}m-6\right)$$

Add $3$ and $2$ to get $5$.

$$\frac{51}{28}m-\frac{51}{8}-\frac{5}{3}\left(\frac{9}{5}m-6\right)$$

Use the distributive property to multiply $-\frac{5}{3}$ by $\frac{9}{5}m-6$.

$$\frac{51}{28}m-\frac{51}{8}-\frac{5}{3}\times \frac{9}{5}m-\frac{5}{3}\left(-6\right)$$

Multiply $-\frac{5}{3}$ times $\frac{9}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{51}{28}m-\frac{51}{8}+\frac{-5\times 9}{3\times 5}m-\frac{5}{3}\left(-6\right)$$

Do the multiplications in the fraction $\frac{-5\times 9}{3\times 5}$.

$$\frac{51}{28}m-\frac{51}{8}+\frac{-45}{15}m-\frac{5}{3}\left(-6\right)$$

Divide $-45$ by $15$ to get $-3$.

$$\frac{51}{28}m-\frac{51}{8}-3m-\frac{5}{3}\left(-6\right)$$

Express $-\frac{5}{3}\left(-6\right)$ as a single fraction.

$$\frac{51}{28}m-\frac{51}{8}-3m+\frac{-5\left(-6\right)}{3}$$

Multiply $-5$ and $-6$ to get $30$.

$$\frac{51}{28}m-\frac{51}{8}-3m+\frac{30}{3}$$

Divide $30$ by $3$ to get $10$.

$$\frac{51}{28}m-\frac{51}{8}-3m+10$$

Combine $\frac{51}{28}m$ and $-3m$ to get $-\frac{33}{28}m$.

$$-\frac{33}{28}m-\frac{51}{8}+10$$

Convert $10$ to fraction $\frac{80}{8}$.

$$-\frac{33}{28}m-\frac{51}{8}+\frac{80}{8}$$

Since $-\frac{51}{8}$ and $\frac{80}{8}$ have the same denominator, add them by adding their numerators.

$$-\frac{33}{28}m+\frac{-51+80}{8}$$

Add $-51$ and $80$ to get $29$.

$$-\frac{33}{28}m+\frac{29}{8}$$

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