Finite Math Examples

$(x + 2) (x - 4) = (x - 1) (x - 3)$

Step 1

Simplify $(x + 2) (x - 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + (x + 2) (x - 4) = (x - 1) (x - 3)$

Step 1.2

Simplify by adding zeros.

$(x + 2) (x - 4) = (x - 1) (x - 3)$

Step 1.3

Expand $(x + 2) (x - 4)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$x (x - 4) + 2 (x - 4) = (x - 1) (x - 3)$

Step 1.3.2

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 2 (x - 4) = (x - 1) (x - 3)$

Step 1.3.3

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 2 x + 2 \cdot - 4 = (x - 1) (x - 3)$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 + 2 x + 2 \cdot - 4 = (x - 1) (x - 3)$

Step 1.4.1.2

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x + 2 x + 2 \cdot - 4 = (x - 1) (x - 3)$

Step 1.4.1.3

Multiply $2$ by $- 4$ .

$x^{2} - 4 x + 2 x - 8 = (x - 1) (x - 3)$

Step 1.4.2

Add $- 4 x$ and $2 x$ .

$x^{2} - 2 x - 8 = (x - 1) (x - 3)$

Step 2

Simplify $(x - 1) (x - 3)$ .

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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.

$x^{2} - 2 x - 8 = x (x - 3) - 1 (x - 3)$

Step 2.1.2

Apply the distributive property.

$x^{2} - 2 x - 8 = x \cdot x + x \cdot - 3 - 1 (x - 3)$

Step 2.1.3

Apply the distributive property.

$x^{2} - 2 x - 8 = x \cdot x + x \cdot - 3 - 1 x - 1 \cdot - 3$

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 $x$ .

$x^{2} - 2 x - 8 = x^{2} + x \cdot - 3 - 1 x - 1 \cdot - 3$

Step 2.2.1.2

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

$x^{2} - 2 x - 8 = x^{2} - 3 \cdot x - 1 x - 1 \cdot - 3$

Step 2.2.1.3

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

$x^{2} - 2 x - 8 = x^{2} - 3 x - x - 1 \cdot - 3$

Step 2.2.1.4

Multiply $- 1$ by $- 3$ .

$x^{2} - 2 x - 8 = x^{2} - 3 x - x + 3$

Step 2.2.2

Subtract $x$ from $- 3 x$ .

$x^{2} - 2 x - 8 = x^{2} - 4 x + 3$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $x^{2}$ from both sides of the equation.

$x^{2} - 2 x - 8 - x^{2} = - 4 x + 3$

Step 3.2

Add $4 x$ to both sides of the equation.

$x^{2} - 2 x - 8 - x^{2} + 4 x = 3$

Step 3.3

Combine the opposite terms in $x^{2} - 2 x - 8 - x^{2} + 4 x$ .

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Step 3.3.1

Subtract $x^{2}$ from $x^{2}$ .

$- 2 x - 8 + 0 + 4 x = 3$

Step 3.3.2

Add $- 2 x - 8$ and $0$ .

$- 2 x - 8 + 4 x = 3$

Step 3.4

Add $- 2 x$ and $4 x$ .

$2 x - 8 = 3$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $8$ to both sides of the equation.

$2 x = 3 + 8$

Step 4.2

Add $3$ and $8$ .

$2 x = 11$

Step 5

Divide each term in $2 x = 11$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = 11$ by $2$ .

$\frac{2 x}{2} = \frac{11}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{11}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{11}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{2}$

Decimal Form:

$x = 5.5$

Mixed Number Form:

$x = 5 \frac{1}{2}$