Basic Math Examples

$2 (z - 4) = 3 (z - 5)$

Step 1

Simplify $2 (z - 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 (z - 4) = 3 (z - 5)$

Step 1.2

Simplify by adding zeros.

$2 (z - 4) = 3 (z - 5)$

Step 1.3

Apply the distributive property.

$2 z + 2 \cdot - 4 = 3 (z - 5)$

Step 1.4

Multiply $2$ by $- 4$ .

$2 z - 8 = 3 (z - 5)$

Step 2

Simplify $3 (z - 5)$ .

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Step 2.1

Apply the distributive property.

$2 z - 8 = 3 z + 3 \cdot - 5$

Step 2.2

Multiply $3$ by $- 5$ .

$2 z - 8 = 3 z - 15$

Step 3

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

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Step 3.1

Subtract $3 z$ from both sides of the equation.

$2 z - 8 - 3 z = - 15$

Step 3.2

Subtract $3 z$ from $2 z$ .

$- z - 8 = - 15$

Step 4

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

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Step 4.1

Add $8$ to both sides of the equation.

$- z = - 15 + 8$

Step 4.2

Add $- 15$ and $8$ .

$- z = - 7$

Step 5

Divide each term in $- z = - 7$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- z = - 7$ by $- 1$ .

$\frac{- z}{- 1} = \frac{- 7}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{- 7}{- 1}$

Step 5.2.2

Divide $z$ by $1$ .

$z = \frac{- 7}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 7$ by $- 1$ .

$z = 7$