Basic Math Examples

$- \frac{2}{3} \cdot (12 c - 9) + 14$

Step 1

Factor $\frac{1}{3}$ out of each term.

$\frac{1}{3} (- 1 \cdot 2 \cdot (12 c - 9) + 42)$

Step 2

Factor $2$ out of $- 1 \cdot 2 \cdot (12 c - 9) + 42$ .

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Step 2.1

Factor $2$ out of $- 1 \cdot 2 \cdot (12 c - 9)$ .

$\frac{1}{3} \cdot (2 (- 1 \cdot (12 c - 9)) + 42)$

Step 2.2

Factor $2$ out of $42$ .

$\frac{1}{3} \cdot (2 (- 1 \cdot (12 c - 9)) + 2 \cdot 21)$

Step 2.3

Factor $2$ out of $2 (- 1 \cdot (12 c - 9)) + 2 \cdot 21$ .

$\frac{1}{3} \cdot (2 (- 1 \cdot (12 c - 9) + 21))$

$\frac{1}{3} \cdot (2 (- 1 (12 c - 9) + 21))$

Step 3

Apply the distributive property.

$\frac{1}{3} \cdot (2 (- 1 (12 c) - 1 \cdot - 9 + 21))$

Step 4

Multiply $12$ by $- 1$ .

$\frac{1}{3} \cdot (2 (- 12 c - 1 \cdot - 9 + 21))$

Step 5

Multiply $- 1$ by $- 9$ .

$\frac{1}{3} \cdot (2 (- 12 c + 9 + 21))$

Step 6

Add $9$ and $21$ .

$\frac{1}{3} \cdot (2 (- 12 c + 30))$

Step 7

Factor.

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Step 7.1

Factor $6$ out of $- 12 c + 30$ .

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Step 7.1.1

Factor $6$ out of $- 12 c$ .

$\frac{1}{3} \cdot (2 (6 (- 2 c) + 30))$

Step 7.1.2

Factor $6$ out of $30$ .

$\frac{1}{3} \cdot (2 (6 (- 2 c) + 6 (5)))$

Step 7.1.3

Factor $6$ out of $6 (- 2 c) + 6 (5)$ .

$\frac{1}{3} \cdot (2 (6 (- 2 c + 5)))$

Step 7.2

Remove unnecessary parentheses.

$\frac{1}{3} \cdot (2 \cdot 6 (- 2 c + 5))$

Step 8

Factor.

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Step 8.1

Multiply $2$ by $6$ .

$\frac{1}{3} \cdot (12 (- 2 c + 5))$

Step 8.2

Remove unnecessary parentheses.

$\frac{1}{3} \cdot 12 (- 2 c + 5)$

Step 9

Combine $\frac{1}{3}$ and $12$ .

$\frac{12}{3} (- 2 c + 5)$

Step 10

Divide $12$ by $3$ .

$4 \cdot (- 2 c + 5)$

Step 11

Factor.

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Step 11.1

Factor $- 1$ out of $- 2 c + 5$ .

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Step 11.1.1

Factor $- 1$ out of $- 2 c$ .

$4 \cdot (- (2 c) + 5)$

Step 11.1.2

Rewrite $5$ as $- 1 (- 5)$ .

$4 \cdot (- (2 c) - 1 (- 5))$

Step 11.1.3

Factor $- 1$ out of $- (2 c) - 1 (- 5)$ .

$4 \cdot (- (2 c - 5))$

Step 11.2

Remove unnecessary parentheses.

$4 \cdot - 1 (2 c - 5)$

Step 12

Combine exponents.

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Step 12.1

Factor out negative.

$- (4 (2 c - 5))$

Step 12.2

Multiply $4$ by $- 1$ .

$- 4 (2 c - 5)$