Basic Math Examples

$20 q + 60 = q^{2} - 8 q$

Step 1

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

$q^{2} - 8 q = 20 q + 60$

Step 2

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

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Step 2.1

Subtract $20 q$ from both sides of the equation.

$q^{2} - 8 q - 20 q = 60$

Step 2.2

Subtract $20 q$ from $- 8 q$ .

$q^{2} - 28 q = 60$

Step 3

Subtract $60$ from both sides of the equation.

$q^{2} - 28 q - 60 = 0$

Step 4

Factor $q^{2} - 28 q - 60$ 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 $- 60$ and whose sum is $- 28$ .

$- 30, 2$

Step 4.2

Write the factored form using these integers.

$(q - 30) (q + 2) = 0$

Step 5

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

$q - 30 = 0$

$q + 2 = 0$

Step 6

Set $q - 30$ equal to $0$ and solve for $q$ .

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Step 6.1

Set $q - 30$ equal to $0$ .

$q - 30 = 0$

Step 6.2

Add $30$ to both sides of the equation.

$q = 30$

Step 7

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

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Step 7.1

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

$q + 2 = 0$

Step 7.2

Subtract $2$ from both sides of the equation.

$q = - 2$

Step 8

The final solution is all the values that make $(q - 30) (q + 2) = 0$ true.

$q = 30, - 2$