Pre-Algebra Examples

$(x - 15) (x + 8) = - 90$

Step 1

Simplify $(x - 15) (x + 8)$ .

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Step 1.1

Expand $(x - 15) (x + 8)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$x (x + 8) - 15 (x + 8) = - 90$

Step 1.1.2

Apply the distributive property.

$x \cdot x + x \cdot 8 - 15 (x + 8) = - 90$

Step 1.1.3

Apply the distributive property.

$x \cdot x + x \cdot 8 - 15 x - 15 \cdot 8 = - 90$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 8 - 15 x - 15 \cdot 8 = - 90$

Step 1.2.1.2

Move $8$ to the left of $x$ .

$x^{2} + 8 \cdot x - 15 x - 15 \cdot 8 = - 90$

Step 1.2.1.3

Multiply $- 15$ by $8$ .

$x^{2} + 8 x - 15 x - 120 = - 90$

Step 1.2.2

Subtract $15 x$ from $8 x$ .

$x^{2} - 7 x - 120 = - 90$

Step 2

Add $90$ to both sides of the equation.

$x^{2} - 7 x - 120 + 90 = 0$

Step 3

Add $- 120$ and $90$ .

$x^{2} - 7 x - 30 = 0$

Step 4

Factor $x^{2} - 7 x - 30$ using the AC method.

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Step 4.1

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 $- 30$ and whose sum is $- 7$ .

$- 10, 3$

Step 4.2

Write the factored form using these integers.

$(x - 10) (x + 3) = 0$

Step 5

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

$x - 10 = 0$

$x + 3 = 0$

Step 6

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

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Step 6.1

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

$x - 10 = 0$

Step 6.2

Add $10$ to both sides of the equation.

$x = 10$

Step 7

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

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Step 7.1

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

$x + 3 = 0$

Step 7.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 8

The final solution is all the values that make $(x - 10) (x + 3) = 0$ true.

$x = 10, - 3$