Algebra Examples

$\frac{5 x^{2} - 25 x}{x}$

Step 1

Set $\frac{5 x^{2} - 25 x}{x}$ equal to $0$ .

$\frac{5 x^{2} - 25 x}{x} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

$5 x^{2} - 25 x = 0$

Step 2.2

Solve the equation for $x$ .

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Step 2.2.1

Factor $5 x$ out of $5 x^{2} - 25 x$ .

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Step 2.2.1.1

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

$5 x (x) - 25 x = 0$

Step 2.2.1.2

Factor $5 x$ out of $- 25 x$ .

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

Step 2.2.1.3

Factor $5 x$ out of $5 x (x) + 5 x (- 5)$ .

$5 x (x - 5) = 0$

Step 2.2.2

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 2.2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.2.4

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

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Step 2.2.4.1

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

$x - 5 = 0$

Step 2.2.4.2

Add $5$ to both sides of the equation.

$x = 5$

Step 2.2.5

The final solution is all the values that make $5 x (x - 5) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 0$ (Multiplicity of $1$ )

$x = 5$ (Multiplicity of $1$ )

$x = 0$ (Multiplicity of $1$ )

$x = 5$ (Multiplicity of $1$ )

Step 2.3

Exclude the solutions that do not make $\frac{5 x^{2} - 25 x}{x} = 0$ true.

$x = 5$ (Multiplicity of $1$ )

Step 3