Algebra Examples

$(x - 7) (x^{2} - 5 x)$

Step 1

Set $(x - 7) (x^{2} - 5 x)$ equal to $0$ .

$(x - 7) (x^{2} - 5 x) = 0$

Step 2

Solve for $x$ .

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Step 2.1

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

$x - 7 = 0$

$x^{2} - 5 x = 0$

Step 2.2

Set $x - 7$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Step 2.2.2

Add $7$ to both sides of the equation.

$x = 7$

Step 2.3

Set $x^{2} - 5 x$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x^{2} - 5 x$ equal to $0$ .

$x^{2} - 5 x = 0$

Step 2.3.2

Solve $x^{2} - 5 x = 0$ for $x$ .

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Step 2.3.2.1

Factor $x$ out of $x^{2} - 5 x$ .

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Step 2.3.2.1.1

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

$x \cdot x - 5 x = 0$

Step 2.3.2.1.2

Factor $x$ out of $- 5 x$ .

$x \cdot x + x \cdot - 5 = 0$

Step 2.3.2.1.3

Factor $x$ out of $x \cdot x + x \cdot - 5$ .

$x (x - 5) = 0$

Step 2.3.2.2

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

$x = 0$

$x - 5 = 0$

Step 2.3.2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.3.2.4

Set $x - 5$ equal to $0$ and solve for $x$ .

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Step 2.3.2.4.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Step 2.3.2.4.2

Add $5$ to both sides of the equation.

$x = 5$

Step 2.3.2.5

The final solution is all the values that make $x (x - 5) = 0$ true.

$x = 0, 5$

Step 2.4

The final solution is all the values that make $(x - 7) (x^{2} - 5 x) = 0$ true.

$x = 7, 0, 5$

Step 3