Basic Math Examples

$9 (5 z + 1) = 5 z - 8 z$

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.

$5 z - 8 z = 9 (5 z + 1)$

Step 2

Subtract $8 z$ from $5 z$ .

$- 3 z = 9 (5 z + 1)$

Step 3

Simplify $9 (5 z + 1)$ .

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Step 3.1

Apply the distributive property.

$- 3 z = 9 (5 z) + 9 \cdot 1$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $5$ by $9$ .

$- 3 z = 45 z + 9 \cdot 1$

Step 3.2.2

Multiply $9$ by $1$ .

$- 3 z = 45 z + 9$

Step 4

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

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Step 4.1

Subtract $45 z$ from both sides of the equation.

$- 3 z - 45 z = 9$

Step 4.2

Subtract $45 z$ from $- 3 z$ .

$- 48 z = 9$

Step 5

Divide each term in $- 48 z = 9$ by $- 48$ and simplify.

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Step 5.1

Divide each term in $- 48 z = 9$ by $- 48$ .

$\frac{- 48 z}{- 48} = \frac{9}{- 48}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 48$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 48 z}{- 48} = \frac{9}{- 48}$

Step 5.2.1.2

Divide $z$ by $1$ .

$z = \frac{9}{- 48}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $9$ and $- 48$ .

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Step 5.3.1.1

Factor $3$ out of $9$ .

$z = \frac{3 (3)}{- 48}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $3$ out of $- 48$ .

$z = \frac{3 \cdot 3}{3 \cdot - 16}$

Step 5.3.1.2.2

Cancel the common factor.

$z = \frac{3 \cdot 3}{3 \cdot - 16}$

Step 5.3.1.2.3

Rewrite the expression.

$z = \frac{3}{- 16}$

Step 5.3.2

Move the negative in front of the fraction.

$z = - \frac{3}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{3}{16}$

Decimal Form:

$z = - 0.1875$