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.

Solve 2 ๆ 8 | Equatix

Question

$$\frac { - 2 } { 5 } \times \frac { 3 } { 7 } - \frac { 4 } { 5 } \times \frac { 1 } { 6 } + \frac { 5 } { 7 } \times \frac { - 2 } { 5 }$$

Evaluate

$-\frac{62}{105}\approx -0.59047619$

Solution Steps

Fraction $\frac{-2}{5}$ can be rewritten as $-\frac{2}{5}$ by extracting the negative sign.

$$-\frac{2}{5}\times \frac{3}{7}-\frac{4}{5}\times \frac{1}{6}+\frac{5}{7}\times \frac{-2}{5}$$

Multiply $-\frac{2}{5}$ times $\frac{3}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 3}{5\times 7}-\frac{4}{5}\times \frac{1}{6}+\frac{5}{7}\times \frac{-2}{5}$$

Do the multiplications in the fraction $\frac{-2\times 3}{5\times 7}$.

$$\frac{-6}{35}-\frac{4}{5}\times \frac{1}{6}+\frac{5}{7}\times \frac{-2}{5}$$

Fraction $\frac{-6}{35}$ can be rewritten as $-\frac{6}{35}$ by extracting the negative sign.

$$-\frac{6}{35}-\frac{4}{5}\times \frac{1}{6}+\frac{5}{7}\times \frac{-2}{5}$$

Multiply $\frac{4}{5}$ times $\frac{1}{6}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{6}{35}-\frac{4\times 1}{5\times 6}+\frac{5}{7}\times \frac{-2}{5}$$

Do the multiplications in the fraction $\frac{4\times 1}{5\times 6}$.

$$-\frac{6}{35}-\frac{4}{30}+\frac{5}{7}\times \frac{-2}{5}$$

Reduce the fraction $\frac{4}{30}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{6}{35}-\frac{2}{15}+\frac{5}{7}\times \frac{-2}{5}$$

Least common multiple of $35$ and $15$ is $105$. Convert $-\frac{6}{35}$ and $\frac{2}{15}$ to fractions with denominator $105$.

$$-\frac{18}{105}-\frac{14}{105}+\frac{5}{7}\times \frac{-2}{5}$$

Since $-\frac{18}{105}$ and $\frac{14}{105}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-18-14}{105}+\frac{5}{7}\times \frac{-2}{5}$$

Subtract $14$ from $-18$ to get $-32$.

$$-\frac{32}{105}+\frac{5}{7}\times \frac{-2}{5}$$

Fraction $\frac{-2}{5}$ can be rewritten as $-\frac{2}{5}$ by extracting the negative sign.

$$-\frac{32}{105}+\frac{5}{7}\left(-\frac{2}{5}\right)$$

Multiply $\frac{5}{7}$ times $-\frac{2}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{32}{105}+\frac{5\left(-2\right)}{7\times 5}$$

Cancel out $5$ in both numerator and denominator.

$$-\frac{32}{105}+\frac{-2}{7}$$

Fraction $\frac{-2}{7}$ can be rewritten as $-\frac{2}{7}$ by extracting the negative sign.

$$-\frac{32}{105}-\frac{2}{7}$$

Least common multiple of $105$ and $7$ is $105$. Convert $-\frac{32}{105}$ and $\frac{2}{7}$ to fractions with denominator $105$.

$$-\frac{32}{105}-\frac{30}{105}$$

Since $-\frac{32}{105}$ and $\frac{30}{105}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-32-30}{105}$$

Subtract $30$ from $-32$ to get $-62$.

$$-\frac{62}{105}$$

Show Solution

Factor

$-\frac{62}{105} = -0.5904761904761905$

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