Basic Math Examples

$\frac{1}{5} \cdot (45 n + 100) = \frac{1}{3} \cdot (27 n - 63)$

Step 1

Simplify $\frac{1}{5} \cdot (45 n + 100)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{5} \cdot (45 n + 100) = \frac{1}{3} \cdot (27 n - 63)$

Step 1.2

Simplify by adding zeros.

$\frac{1}{5} \cdot (45 n + 100) = \frac{1}{3} \cdot (27 n - 63)$

Step 1.3

Apply the distributive property.

$\frac{1}{5} (45 n) + \frac{1}{5} \cdot 100 = \frac{1}{3} \cdot (27 n - 63)$

Step 1.4

Cancel the common factor of $5$ .

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Step 1.4.1

Factor $5$ out of $45 n$ .

$\frac{1}{5} (5 (9 n)) + \frac{1}{5} \cdot 100 = \frac{1}{3} \cdot (27 n - 63)$

Step 1.4.2

Cancel the common factor.

$\frac{1}{5} (5 (9 n)) + \frac{1}{5} \cdot 100 = \frac{1}{3} \cdot (27 n - 63)$

Step 1.4.3

Rewrite the expression.

$9 n + \frac{1}{5} \cdot 100 = \frac{1}{3} \cdot (27 n - 63)$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Factor $5$ out of $100$ .

$9 n + \frac{1}{5} \cdot (5 (20)) = \frac{1}{3} \cdot (27 n - 63)$

Step 1.5.2

Cancel the common factor.

$9 n + \frac{1}{5} \cdot (5 \cdot 20) = \frac{1}{3} \cdot (27 n - 63)$

Step 1.5.3

Rewrite the expression.

$9 n + 20 = \frac{1}{3} \cdot (27 n - 63)$

Step 2

Simplify $\frac{1}{3} \cdot (27 n - 63)$ .

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Step 2.1

Apply the distributive property.

$9 n + 20 = \frac{1}{3} (27 n) + \frac{1}{3} \cdot - 63$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Factor $3$ out of $27 n$ .

$9 n + 20 = \frac{1}{3} (3 (9 n)) + \frac{1}{3} \cdot - 63$

Step 2.2.2

Cancel the common factor.

$9 n + 20 = \frac{1}{3} (3 (9 n)) + \frac{1}{3} \cdot - 63$

Step 2.2.3

Rewrite the expression.

$9 n + 20 = 9 n + \frac{1}{3} \cdot - 63$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Factor $3$ out of $- 63$ .

$9 n + 20 = 9 n + \frac{1}{3} \cdot (3 (- 21))$

Step 2.3.2

Cancel the common factor.

$9 n + 20 = 9 n + \frac{1}{3} \cdot (3 \cdot - 21)$

Step 2.3.3

Rewrite the expression.

$9 n + 20 = 9 n - 21$

Step 3

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

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Step 3.1

Subtract $9 n$ from both sides of the equation.

$9 n + 20 - 9 n = - 21$

Step 3.2

Combine the opposite terms in $9 n + 20 - 9 n$ .

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Step 3.2.1

Subtract $9 n$ from $9 n$ .

$0 + 20 = - 21$

Step 3.2.2

Add $0$ and $20$ .

$20 = - 21$

Step 4

Since $20 \neq - 21$ , there are no solutions.

No solution