Basic Math Examples

$z^{2} - 5 z = z (3 + z)$

Step 1

Simplify $z (3 + z)$ .

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Step 1.1

Apply the distributive property.

$z^{2} - 5 z = z \cdot 3 + z \cdot z$

Step 1.2

Simplify the expression.

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Step 1.2.1

Move $3$ to the left of $z$ .

$z^{2} - 5 z = 3 \cdot z + z \cdot z$

Step 1.2.2

Multiply $z$ by $z$ .

$z^{2} - 5 z = 3 z + z^{2}$

Step 2

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

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Step 2.1

Subtract $3 z$ from both sides of the equation.

$z^{2} - 5 z - 3 z = z^{2}$

Step 2.2

Subtract $z^{2}$ from both sides of the equation.

$z^{2} - 5 z - 3 z - z^{2} = 0$

Step 2.3

Combine the opposite terms in $z^{2} - 5 z - 3 z - z^{2}$ .

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Step 2.3.1

Subtract $z^{2}$ from $z^{2}$ .

$- 5 z - 3 z + 0 = 0$

Step 2.3.2

Add $- 5 z - 3 z$ and $0$ .

$- 5 z - 3 z = 0$

Step 2.4

Subtract $3 z$ from $- 5 z$ .

$- 8 z = 0$

Step 3

Divide each term in $- 8 z = 0$ by $- 8$ and simplify.

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Step 3.1

Divide each term in $- 8 z = 0$ by $- 8$ .

$\frac{- 8 z}{- 8} = \frac{0}{- 8}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 8$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 8 z}{- 8} = \frac{0}{- 8}$

Step 3.2.1.2

Divide $z$ by $1$ .

$z = \frac{0}{- 8}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $- 8$ .

$z = 0$