Algebra Examples

$f (x) = x (x + 2) (x - 3)$

Step 1

Set $x (x + 2) (x - 3)$ equal to $0$ .

$x (x + 2) (x - 3) = 0$

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 $0$ .

$x = 0$

$x + 2 = 0$

$x - 3 = 0$

Step 2.2

Set $x$ equal to $0$ .

$x = 0$

Step 2.3

Set $x + 2$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Step 2.3.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 2.4

Set $x - 3$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Step 2.4.2

Add $3$ to both sides of the equation.

$x = 3$

Step 2.5

The final solution is all the values that make $x (x + 2) (x - 3) = 0$ true. The multiplicity of a root is the number of times the root appears.

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

$x = - 2$ (Multiplicity of $1$ )

$x = 3$ (Multiplicity of $1$ )

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

$x = - 2$ (Multiplicity of $1$ )

$x = 3$ (Multiplicity of $1$ )

Step 3