Algebra Examples

$\frac{4 z}{- 12} = - 8$

Step 1

Cancel the common factor of $4$ and $- 12$ .

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Step 1.1

Factor $4$ out of $4 z$ .

$\frac{4 (z)}{- 12} = - 8$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $- 12$ .

$\frac{4 z}{4 \cdot - 3} = - 8$

Step 1.2.2

Cancel the common factor.

$\frac{4 z}{4 \cdot - 3} = - 8$

Step 1.2.3

Rewrite the expression.

$\frac{z}{- 3} = - 8$

Step 2

Multiply both sides by $- 3$ .

$\frac{z}{- 3} \cdot - 3 = - 8 \cdot - 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{z}{- 3} \cdot - 3$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Factor $3$ out of $- 3$ .

$\frac{z}{3 (- 1)} \cdot - 3 = - 8 \cdot - 3$

Step 3.1.1.1.2

Factor $3$ out of $- 3$ .

$\frac{z}{3 \cdot - 1} \cdot (3 \cdot - 1) = - 8 \cdot - 3$

Step 3.1.1.1.3

Cancel the common factor.

$\frac{z}{3 \cdot - 1} \cdot (3 \cdot - 1) = - 8 \cdot - 3$

Step 3.1.1.1.4

Rewrite the expression.

$\frac{z}{- 1} \cdot - 1 = - 8 \cdot - 3$

Step 3.1.1.2

Combine $\frac{z}{- 1}$ and $- 1$ .

$\frac{z \cdot - 1}{- 1} = - 8 \cdot - 3$

Step 3.1.1.3

Simplify the expression.

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Step 3.1.1.3.1

Move the negative one from the denominator of $\frac{z \cdot - 1}{- 1}$ .

$- 1 \cdot (z \cdot - 1) = - 8 \cdot - 3$

Step 3.1.1.3.2

Rewrite $- 1 \cdot (z \cdot - 1)$ as $- (z \cdot - 1)$ .

$- (z \cdot - 1) = - 8 \cdot - 3$

Step 3.1.1.3.3

Move $- 1$ to the left of $z$ .

$- (- 1 \cdot z) = - 8 \cdot - 3$

Step 3.1.1.3.4

Rewrite $- 1 z$ as $- z$ .

$- - z = - 8 \cdot - 3$

Step 3.1.1.4

Multiply $- - z$ .

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Step 3.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 z = - 8 \cdot - 3$

Step 3.1.1.4.2

Multiply $z$ by $1$ .

$z = - 8 \cdot - 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 8$ by $- 3$ .

$z = 24$