Basic Math Examples

$9 (z - (5 z + 29) + 5) = 4 (z + 6)$

Step 1

Simplify $9 (z - (5 z + 29) + 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + 9 (z - (5 z + 29) + 5) = 4 (z + 6)$

Step 1.2

Simplify by adding zeros.

$9 (z - (5 z + 29) + 5) = 4 (z + 6)$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$9 (z - (5 z) - 1 \cdot 29 + 5) = 4 (z + 6)$

Step 1.3.2

Multiply $5$ by $- 1$ .

$9 (z - 5 z - 1 \cdot 29 + 5) = 4 (z + 6)$

Step 1.3.3

Multiply $- 1$ by $29$ .

$9 (z - 5 z - 29 + 5) = 4 (z + 6)$

Step 1.4

Simplify terms.

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Step 1.4.1

Subtract $5 z$ from $z$ .

$9 (- 4 z - 29 + 5) = 4 (z + 6)$

Step 1.4.2

Add $- 29$ and $5$ .

$9 (- 4 z - 24) = 4 (z + 6)$

Step 1.4.3

Apply the distributive property.

$9 (- 4 z) + 9 \cdot - 24 = 4 (z + 6)$

Step 1.4.4

Multiply.

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Step 1.4.4.1

Multiply $- 4$ by $9$ .

$- 36 z + 9 \cdot - 24 = 4 (z + 6)$

Step 1.4.4.2

Multiply $9$ by $- 24$ .

$- 36 z - 216 = 4 (z + 6)$

Step 2

Simplify $4 (z + 6)$ .

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Step 2.1

Apply the distributive property.

$- 36 z - 216 = 4 z + 4 \cdot 6$

Step 2.2

Multiply $4$ by $6$ .

$- 36 z - 216 = 4 z + 24$

Step 3

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

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Step 3.1

Subtract $4 z$ from both sides of the equation.

$- 36 z - 216 - 4 z = 24$

Step 3.2

Subtract $4 z$ from $- 36 z$ .

$- 40 z - 216 = 24$

Step 4

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

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Step 4.1

Add $216$ to both sides of the equation.

$- 40 z = 24 + 216$

Step 4.2

Add $24$ and $216$ .

$- 40 z = 240$

Step 5

Divide each term in $- 40 z = 240$ by $- 40$ and simplify.

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Step 5.1

Divide each term in $- 40 z = 240$ by $- 40$ .

$\frac{- 40 z}{- 40} = \frac{240}{- 40}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 40$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 40 z}{- 40} = \frac{240}{- 40}$

Step 5.2.1.2

Divide $z$ by $1$ .

$z = \frac{240}{- 40}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $240$ by $- 40$ .

$z = - 6$