Basic Math Examples

$z^{2} = 15 z$

Step 1

Subtract $15 z$ from both sides of the equation.

$z^{2} - 15 z = 0$

Step 2

Factor $z$ out of $z^{2} - 15 z$ .

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Step 2.1

Factor $z$ out of $z^{2}$ .

$z \cdot z - 15 z = 0$

Step 2.2

Factor $z$ out of $- 15 z$ .

$z \cdot z + z \cdot - 15 = 0$

Step 2.3

Factor $z$ out of $z \cdot z + z \cdot - 15$ .

$z (z - 15) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$z = 0$

$z - 15 = 0$

Step 4

Set $z$ equal to $0$ .

$z = 0$

Step 5

Set $z - 15$ equal to $0$ and solve for $z$ .

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Step 5.1

Set $z - 15$ equal to $0$ .

$z - 15 = 0$

Step 5.2

Add $15$ to both sides of the equation.

$z = 15$

Step 6

The final solution is all the values that make $z (z - 15) = 0$ true.

$z = 0, 15$