Finite Math Examples

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

Step 1

Simplify $(x - 4) (x - 3)$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Expand $(x - 4) (x - 3)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Apply the distributive property.

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

Step 1.3.3

Apply the distributive property.

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

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 $x$ .

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

Step 1.4.1.2

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

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

Step 1.4.1.3

Multiply $- 4$ by $- 3$ .

$x^{2} - 3 x - 4 x + 12 = x^{2} - x + 4$

Step 1.4.2

Subtract $4 x$ from $- 3 x$ .

$x^{2} - 7 x + 12 = x^{2} - x + 4$

Step 2

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

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Step 2.1

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

$x^{2} - 7 x + 12 - x^{2} = - x + 4$

Step 2.2

Add $x$ to both sides of the equation.

$x^{2} - 7 x + 12 - x^{2} + x = 4$

Step 2.3

Combine the opposite terms in $x^{2} - 7 x + 12 - x^{2} + x$ .

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Step 2.3.1

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

$- 7 x + 12 + 0 + x = 4$

Step 2.3.2

Add $- 7 x + 12$ and $0$ .

$- 7 x + 12 + x = 4$

Step 2.4

Add $- 7 x$ and $x$ .

$- 6 x + 12 = 4$

Step 3

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

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Step 3.1

Subtract $12$ from both sides of the equation.

$- 6 x = 4 - 12$

Step 3.2

Subtract $12$ from $4$ .

$- 6 x = - 8$

Step 4

Divide each term in $- 6 x = - 8$ by $- 6$ and simplify.

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Step 4.1

Divide each term in $- 6 x = - 8$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 8}{- 6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 8}{- 6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 8$ and $- 6$ .

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Step 4.3.1.1

Factor $- 2$ out of $- 8$ .

$x = \frac{- 2 (4)}{- 6}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $- 2$ out of $- 6$ .

$x = \frac{- 2 \cdot 4}{- 2 \cdot 3}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{- 2 \cdot 4}{- 2 \cdot 3}$

Step 4.3.1.2.3

Rewrite the expression.

$x = \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{3}$

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

$x = 1 \frac{1}{3}$