Basic Math Examples

$z - 52 = - \frac{3}{2} \cdot (18 + z)$

Step 1

Simplify $- \frac{3}{2} \cdot (18 + z)$ .

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Step 1.1

Rewrite.

$z - 52 = 0 + 0 - \frac{3}{2} \cdot (18 + z)$

Step 1.2

Simplify terms.

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Step 1.2.1

Apply the distributive property.

$z - 52 = - \frac{3}{2} \cdot 18 - \frac{3}{2} z$

Step 1.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$z - 52 = \frac{- 3}{2} \cdot 18 - \frac{3}{2} z$

Step 1.2.2.2

Factor $2$ out of $18$ .

$z - 52 = \frac{- 3}{2} \cdot (2 (9)) - \frac{3}{2} z$

Step 1.2.2.3

Cancel the common factor.

$z - 52 = \frac{- 3}{2} \cdot (2 \cdot 9) - \frac{3}{2} z$

Step 1.2.2.4

Rewrite the expression.

$z - 52 = - 3 \cdot 9 - \frac{3}{2} z$

Step 1.2.3

Multiply $- 3$ by $9$ .

$z - 52 = - 27 - \frac{3}{2} z$

Step 1.2.4

Combine $z$ and $\frac{3}{2}$ .

$z - 52 = - 27 - \frac{z \cdot 3}{2}$

Step 1.3

Move $3$ to the left of $z$ .

$z - 52 = - 27 - \frac{3 z}{2}$

Step 2

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

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Step 2.1

Add $\frac{3 z}{2}$ to both sides of the equation.

$z - 52 + \frac{3 z}{2} = - 27$

Step 2.2

To write $z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$z \cdot \frac{2}{2} + \frac{3 z}{2} - 52 = - 27$

Step 2.3

Combine $z$ and $\frac{2}{2}$ .

$\frac{z \cdot 2}{2} + \frac{3 z}{2} - 52 = - 27$

Step 2.4

Combine the numerators over the common denominator.

$\frac{z \cdot 2 + 3 z}{2} - 52 = - 27$

Step 2.5

Add $z \cdot 2$ and $3 z$ .

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Step 2.5.1

Reorder $z$ and $2$ .

$\frac{2 \cdot z + 3 z}{2} - 52 = - 27$

Step 2.5.2

Add $2 \cdot z$ and $3 z$ .

$\frac{5 \cdot z}{2} - 52 = - 27$

$\frac{5 z}{2} - 52 = - 27$

Step 3

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

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Step 3.1

Add $52$ to both sides of the equation.

$\frac{5 z}{2} = - 27 + 52$

Step 3.2

Add $- 27$ and $52$ .

$\frac{5 z}{2} = 25$

Step 4

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 z}{2} = \frac{2}{5} \cdot 25$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{2}{5} \cdot \frac{5 z}{2}$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 z}{2} = \frac{2}{5} \cdot 25$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 z) = \frac{2}{5} \cdot 25$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 z$ .

$\frac{1}{5} (5 (z)) = \frac{2}{5} \cdot 25$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 z) = \frac{2}{5} \cdot 25$

Step 5.1.1.2.3

Rewrite the expression.

$z = \frac{2}{5} \cdot 25$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{2}{5} \cdot 25$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Factor $5$ out of $25$ .

$z = \frac{2}{5} \cdot (5 (5))$

Step 5.2.1.1.2

Cancel the common factor.

$z = \frac{2}{5} \cdot (5 \cdot 5)$

Step 5.2.1.1.3

Rewrite the expression.

$z = 2 \cdot 5$

Step 5.2.1.2

Multiply $2$ by $5$ .

$z = 10$