Pre-Algebra Examples

$14 (x - 4) - (x + 2) = (x + 2) (x - 4)$

Step 1

Simplify $14 (x - 4) - (x + 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$14 x + 14 \cdot - 4 - (x + 2) = (x + 2) (x - 4)$

Step 1.1.2

Multiply $14$ by $- 4$ .

$14 x - 56 - (x + 2) = (x + 2) (x - 4)$

Step 1.1.3

Apply the distributive property.

$14 x - 56 - x - 1 \cdot 2 = (x + 2) (x - 4)$

Step 1.1.4

Multiply $- 1$ by $2$ .

$14 x - 56 - x - 2 = (x + 2) (x - 4)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $x$ from $14 x$ .

$13 x - 56 - 2 = (x + 2) (x - 4)$

Step 1.2.2

Subtract $2$ from $- 56$ .

$13 x - 58 = (x + 2) (x - 4)$

Step 2

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

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Step 2.1

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

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Step 2.1.1

Apply the distributive property.

$13 x - 58 = x (x - 4) + 2 (x - 4)$

Step 2.1.2

Apply the distributive property.

$13 x - 58 = x \cdot x + x \cdot - 4 + 2 (x - 4)$

Step 2.1.3

Apply the distributive property.

$13 x - 58 = x \cdot x + x \cdot - 4 + 2 x + 2 \cdot - 4$

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 $x$ .

$13 x - 58 = x^{2} + x \cdot - 4 + 2 x + 2 \cdot - 4$

Step 2.2.1.2

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

$13 x - 58 = x^{2} - 4 \cdot x + 2 x + 2 \cdot - 4$

Step 2.2.1.3

Multiply $2$ by $- 4$ .

$13 x - 58 = x^{2} - 4 x + 2 x - 8$

Step 2.2.2

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

$13 x - 58 = x^{2} - 2 x - 8$

Step 3

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} - 2 x - 8 = 13 x - 58$

Step 4

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

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Step 4.1

Subtract $13 x$ from both sides of the equation.

$x^{2} - 2 x - 8 - 13 x = - 58$

Step 4.2

Subtract $13 x$ from $- 2 x$ .

$x^{2} - 15 x - 8 = - 58$

Step 5

Add $58$ to both sides of the equation.

$x^{2} - 15 x - 8 + 58 = 0$

Step 6

Add $- 8$ and $58$ .

$x^{2} - 15 x + 50 = 0$

Step 7

Factor $x^{2} - 15 x + 50$ using the AC method.

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Step 7.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $50$ and whose sum is $- 15$ .

$- 10, - 5$

Step 7.2

Write the factored form using these integers.

$(x - 10) (x - 5) = 0$

Step 8

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 10 = 0$

$x - 5 = 0$

Step 9

Set $x - 10$ equal to $0$ and solve for $x$ .

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Step 9.1

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Step 9.2

Add $10$ to both sides of the equation.

$x = 10$

Step 10

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

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Step 10.1

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

$x - 5 = 0$

Step 10.2

Add $5$ to both sides of the equation.

$x = 5$

Step 11

The final solution is all the values that make $(x - 10) (x - 5) = 0$ true.

$x = 10, 5$