Finite Math Examples

$a^{2} + 3 a + 24 = 6 - 6 a$

Step 1

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

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Step 1.1

Add $6 a$ to both sides of the equation.

$a^{2} + 3 a + 24 + 6 a = 6$

Step 1.2

Add $3 a$ and $6 a$ .

$a^{2} + 9 a + 24 = 6$

Step 2

Subtract $6$ from both sides of the equation.

$a^{2} + 9 a + 24 - 6 = 0$

Step 3

Subtract $6$ from $24$ .

$a^{2} + 9 a + 18 = 0$

Step 4

Factor $a^{2} + 9 a + 18$ 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 $18$ and whose sum is $9$ .

$3, 6$

Step 4.2

Write the factored form using these integers.

$(a + 3) (a + 6) = 0$

Step 5

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

$a + 3 = 0$

$a + 6 = 0$

Step 6

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

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Step 6.1

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

$a + 3 = 0$

Step 6.2

Subtract $3$ from both sides of the equation.

$a = - 3$

Step 7

Set $a + 6$ equal to $0$ and solve for $a$ .

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Step 7.1

Set $a + 6$ equal to $0$ .

$a + 6 = 0$

Step 7.2

Subtract $6$ from both sides of the equation.

$a = - 6$

Step 8

The final solution is all the values that make $(a + 3) (a + 6) = 0$ true.

$a = - 3, - 6$