Examples

$x = 1$ , $x = 3$

Step 1

Since the roots of an equation are the points where the solution is $0$ , set each root as a factor of the equation that equals $0$ .

$(x - 1) (x - 3) = 0$

Step 2

Simplify.

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Step 2.1

Expand $(x - 1) (x - 3)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$x (x - 3) - 1 (x - 3) = 0$

Step 2.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 1 (x - 3) = 0$

Step 2.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 1 x - 1 \cdot - 3 = 0$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 - 1 x - 1 \cdot - 3 = 0$

Step 2.2.1.2

Move $- 3$ to the left of $x$ .

$x^{2} - 3 \cdot x - 1 x - 1 \cdot - 3 = 0$

Step 2.2.1.3

Rewrite $- 1 x$ as $- x$ .

$x^{2} - 3 x - x - 1 \cdot - 3 = 0$

Step 2.2.1.4

Multiply $- 1$ by $- 3$ .

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

Step 2.2.2

Subtract $x$ from $- 3 x$ .

$x^{2} - 4 x + 3 = 0$

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