Basic Math Examples

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

Step 1

Simplify $3 (2 z - 4)$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $3$ .

$6 z + 3 \cdot - 4 = - 5 (- 4 - z)$

Step 1.4.2

Multiply $3$ by $- 4$ .

$6 z - 12 = - 5 (- 4 - z)$

Step 2

Simplify $- 5 (- 4 - z)$ .

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Step 2.1

Apply the distributive property.

$6 z - 12 = - 5 \cdot - 4 - 5 (- z)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $- 5$ by $- 4$ .

$6 z - 12 = 20 - 5 (- z)$

Step 2.2.2

Multiply $- 1$ by $- 5$ .

$6 z - 12 = 20 + 5 z$

Step 3

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

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Step 3.1

Subtract $5 z$ from both sides of the equation.

$6 z - 12 - 5 z = 20$

Step 3.2

Subtract $5 z$ from $6 z$ .

$z - 12 = 20$

Step 4

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

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Step 4.1

Add $12$ to both sides of the equation.

$z = 20 + 12$

Step 4.2

Add $20$ and $12$ .

$z = 32$