Algebra Examples

3 x^{2} - 15 x = 0

$3 x^{2} - 15 x = 0$

Step 1

Factor

3 x

$3 x$ out of

3 x^{2} - 15 x

$3 x^{2} - 15 x$ .

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Step 1.1

Factor

3 x

$3 x$ out of

3 x^{2}

$3 x^{2}$ .

3 x (x) - 15 x = 0

$3 x (x) - 15 x = 0$

Step 1.2

Factor

3 x

$3 x$ out of

- 15 x

$- 15 x$ .

3 x (x) + 3 x (- 5) = 0

$3 x (x) + 3 x (- 5) = 0$

Step 1.3

Factor

3 x

$3 x$ out of

3 x (x) + 3 x (- 5)

$3 x (x) + 3 x (- 5)$ .

3 x (x - 5) = 0

$3 x (x - 5) = 0$

3 x (x - 5) = 0

$3 x (x - 5) = 0$

Step 2

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x = 0

$x = 0$

x - 5 = 0

$x - 5 = 0$

Step 3

Set

x

$x$ equal to

0

$0$ .

x = 0

$x = 0$

Step 4

Set

x - 5

$x - 5$ equal to

0

$0$ and solve for

x

$x$ .

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Step 4.1

Set

x - 5

$x - 5$ equal to

0

$0$ .

x - 5 = 0

$x - 5 = 0$

Step 4.2

Add

5

$5$ to both sides of the equation.

x = 5

$x = 5$

x = 5

$x = 5$

Step 5

The final solution is all the values that make

3 x (x - 5) = 0

$3 x (x - 5) = 0$ true.

x = 0, 5

$x = 0, 5$

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