Algebra Examples

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

Step 1

Simplify $2 (3 - 2 (z + 4))$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Multiply $- 2$ by $4$ .

$2 (3 - 2 z - 8) = 3 (4 - z)$

Step 1.4

Simplify by multiplying through.

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Step 1.4.1

Subtract $8$ from $3$ .

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

Step 1.4.2

Apply the distributive property.

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

Step 1.4.3

Multiply.

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Step 1.4.3.1

Multiply $- 2$ by $2$ .

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

Step 1.4.3.2

Multiply $2$ by $- 5$ .

$- 4 z - 10 = 3 (4 - z)$

Step 2

Simplify $3 (4 - z)$ .

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Step 2.1

Apply the distributive property.

$- 4 z - 10 = 3 \cdot 4 + 3 (- z)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $3$ by $4$ .

$- 4 z - 10 = 12 + 3 (- z)$

Step 2.2.2

Multiply $- 1$ by $3$ .

$- 4 z - 10 = 12 - 3 z$

Step 3

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

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Step 3.1

Add $3 z$ to both sides of the equation.

$- 4 z - 10 + 3 z = 12$

Step 3.2

Add $- 4 z$ and $3 z$ .

$- z - 10 = 12$

Step 4

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

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Step 4.1

Add $10$ to both sides of the equation.

$- z = 12 + 10$

Step 4.2

Add $12$ and $10$ .

$- z = 22$

Step 5

Divide each term in $- z = 22$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- z = 22$ by $- 1$ .

$\frac{- z}{- 1} = \frac{22}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{22}{- 1}$

Step 5.2.2

Divide $z$ by $1$ .

$z = \frac{22}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $22$ by $- 1$ .

$z = - 22$