Basic Math Examples

$12 \cdot (a + b + c) = a \cdot b \cdot c$

Step 1

Simplify $12 \cdot (a + b + c)$ .

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Step 1.1

Rewrite.

$0 + 0 + 12 \cdot (a + b + c) = a \cdot b \cdot c$

Step 1.2

Simplify by adding zeros.

$12 \cdot (a + b + c) = a \cdot b \cdot c$

Step 1.3

Apply the distributive property.

$12 a + 12 b + 12 c = a \cdot b \cdot c$

Step 2

Multiply $a b$ by $c$ .

$12 a + 12 b + 12 c = a b c$

Step 3

Subtract $a b c$ from both sides of the equation.

$12 a + 12 b + 12 c - a b c = 0$

Step 4

Move all terms not containing $b$ to the right side of the equation.

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Step 4.1

Subtract $12 a$ from both sides of the equation.

$12 b + 12 c - a b c = - 12 a$

Step 4.2

Subtract $12 c$ from both sides of the equation.

$12 b - a b c = - 12 a - 12 c$

Step 5

Factor $b$ out of $12 b - a b c$ .

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Step 5.1

Factor $b$ out of $12 b$ .

$b \cdot 12 - a b c = - 12 a - 12 c$

Step 5.2

Factor $b$ out of $- a b c$ .

$b \cdot 12 + b (- a c) = - 12 a - 12 c$

Step 5.3

Factor $b$ out of $b \cdot 12 + b (- a c)$ .

$b (12 - a c) = - 12 a - 12 c$

Step 6

Divide each term in $b (12 - a c) = - 12 a - 12 c$ by $12 - a c$ and simplify.

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Step 6.1

Divide each term in $b (12 - a c) = - 12 a - 12 c$ by $12 - a c$ .

$\frac{b (12 - a c)}{12 - a c} = \frac{- 12 a}{12 - a c} + \frac{- 12 c}{12 - a c}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $12 - a c$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{b (12 - a c)}{12 - a c} = \frac{- 12 a}{12 - a c} + \frac{- 12 c}{12 - a c}$

Step 6.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 12 a}{12 - a c} + \frac{- 12 c}{12 - a c}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Combine the numerators over the common denominator.

$b = \frac{- 12 a - 12 c}{12 - a c}$

Step 6.3.2

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

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Step 6.3.2.1

Factor $12$ out of $- 12 a$ .

$b = \frac{12 (- a) - 12 c}{12 - a c}$

Step 6.3.2.2

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

$b = \frac{12 (- a) + 12 (- c)}{12 - a c}$

Step 6.3.2.3

Factor $12$ out of $12 (- a) + 12 (- c)$ .

$b = \frac{12 (- a - c)}{12 - a c}$

Step 6.3.3

Factor $- 1$ out of $- a$ .

$b = \frac{12 (- (a) - c)}{12 - a c}$

Step 6.3.4

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

$b = \frac{12 (- (a) - (c))}{12 - a c}$

Step 6.3.5

Factor $- 1$ out of $- (a) - (c)$ .

$b = \frac{12 (- (a + c))}{12 - a c}$

Step 6.3.6

Simplify the expression.

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Step 6.3.6.1

Rewrite $- (a + c)$ as $- 1 (a + c)$ .

$b = \frac{12 (- 1 (a + c))}{12 - a c}$

Step 6.3.6.2

Move the negative in front of the fraction.

$b = - \frac{12 (a + c)}{12 - a c}$