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 1980/42 | Equatix

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Question

$$1980\div42$$

Evaluate

$\frac{330}{7}\approx 47.142857143$

Steps For Long Division Method

Use the $1^{st}$ digit $1$ from dividend $1980$

$$\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)1980}\\\end{array}$$

Since $1$ is less than $42$, use the next digit $9$ from dividend $1980$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)1980}\\\end{array}$$

Use the $2^{nd}$ digit $9$ from dividend $1980$

$$\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)1980}\\\end{array}$$

Since $19$ is less than $42$, use the next digit $8$ from dividend $1980$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)1980}\\\end{array}$$

Use the $3^{rd}$ digit $8$ from dividend $1980$

$$\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)1980}\\\end{array}$$

Find closest multiple of $42$ to $198$. We see that $4 \times 42 = 168$ is the nearest. Now subtract $168$ from $198$ to get reminder $30$. Add $4$ to quotient.

$$\begin{array}{l}\phantom{42)}004\phantom{6}\\42\overline{)1980}\\\phantom{42)}\underline{\phantom{}168\phantom{9}}\\\phantom{42)9}30\\\end{array}$$

Use the $4^{th}$ digit $0$ from dividend $1980$

$$\begin{array}{l}\phantom{42)}004\phantom{7}\\42\overline{)1980}\\\phantom{42)}\underline{\phantom{}168\phantom{9}}\\\phantom{42)9}300\\\end{array}$$

Find closest multiple of $42$ to $300$. We see that $7 \times 42 = 294$ is the nearest. Now subtract $294$ from $300$ to get reminder $6$. Add $7$ to quotient.

$$\begin{array}{l}\phantom{42)}0047\phantom{8}\\42\overline{)1980}\\\phantom{42)}\underline{\phantom{}168\phantom{9}}\\\phantom{42)9}300\\\phantom{42)}\underline{\phantom{9}294\phantom{}}\\\phantom{42)999}6\\\end{array}$$

Since $6$ is less than $42$, stop the division. The reminder is $6$. The topmost line $0047$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $47$.

$$\text{Quotient: }47$$ $$\text{Reminder: }6$$

Show Solution

Factor

$\frac{2 \cdot 3 \cdot 5 \cdot 11}{7} = 47\frac{1}{7} = 47.142857142857146$