Basic Math Examples

$- 39 - 4 (2 z - 3) = 4 z - 3 (4 - z)$

Step 1

Since $z$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 z - 3 (4 - z) = - 39 - 4 (2 z - 3)$

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 z - 3 \cdot 4 - 3 (- z) = - 39 - 4 (2 z - 3)$

Step 2.1.2

Multiply $- 3$ by $4$ .

$4 z - 12 - 3 (- z) = - 39 - 4 (2 z - 3)$

Step 2.1.3

Multiply $- 1$ by $- 3$ .

$4 z - 12 + 3 z = - 39 - 4 (2 z - 3)$

Step 2.2

Add $4 z$ and $3 z$ .

$7 z - 12 = - 39 - 4 (2 z - 3)$

Step 3

Simplify $- 39 - 4 (2 z - 3)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$7 z - 12 = - 39 - 4 (2 z) - 4 \cdot - 3$

Step 3.1.2

Multiply $2$ by $- 4$ .

$7 z - 12 = - 39 - 8 z - 4 \cdot - 3$

Step 3.1.3

Multiply $- 4$ by $- 3$ .

$7 z - 12 = - 39 - 8 z + 12$

Step 3.2

Add $- 39$ and $12$ .

$7 z - 12 = - 8 z - 27$

Step 4

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

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Step 4.1

Add $8 z$ to both sides of the equation.

$7 z - 12 + 8 z = - 27$

Step 4.2

Add $7 z$ and $8 z$ .

$15 z - 12 = - 27$

Step 5

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

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Step 5.1

Add $12$ to both sides of the equation.

$15 z = - 27 + 12$

Step 5.2

Add $- 27$ and $12$ .

$15 z = - 15$

Step 6

Divide each term in $15 z = - 15$ by $15$ and simplify.

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Step 6.1

Divide each term in $15 z = - 15$ by $15$ .

$\frac{15 z}{15} = \frac{- 15}{15}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $15$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{15 z}{15} = \frac{- 15}{15}$

Step 6.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 15}{15}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 15$ by $15$ .

$z = - 1$