Finite Math Examples

$(x + 5) (x^{2} - 3 x - 10) = 0$

Step 1

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

$x + 5 = 0$

$x^{2} - 3 x - 10 = 0$

Step 2

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

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Step 2.1

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

$x + 5 = 0$

Step 2.2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 3

Set $x^{2} - 3 x - 10$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x^{2} - 3 x - 10$ equal to $0$ .

$x^{2} - 3 x - 10 = 0$

Step 3.2

Solve $x^{2} - 3 x - 10 = 0$ for $x$ .

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Step 3.2.1

Factor $x^{2} - 3 x - 10$ using the AC method.

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Step 3.2.1.1

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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Step 3.2.1.2

Write the factored form using these integers.

$(x - 5) (x + 2) = 0$

Step 3.2.2

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

$x - 5 = 0$

$x + 2 = 0$

Step 3.2.3

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

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Step 3.2.3.1

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

$x - 5 = 0$

Step 3.2.3.2

Add $5$ to both sides of the equation.

$x = 5$

Step 3.2.4

Set $x + 2$ equal to $0$ and solve for $x$ .

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Step 3.2.4.1

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Step 3.2.4.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 3.2.5

The final solution is all the values that make $(x - 5) (x + 2) = 0$ true.

$x = 5, - 2$

Step 4

The final solution is all the values that make $(x + 5) (x^{2} - 3 x - 10) = 0$ true.

$x = - 5, 5, - 2$