Solve by Factoring q+5/q=-6

$q + \frac{5}{q} = - 6$

Step 1

Add $6$ to both sides of the equation.

$q + \frac{5}{q} + 6 = 0$

Step 2

To write $q$ as a fraction with a common denominator, multiply by $\frac{q}{q}$ .

$\frac{q \cdot q}{q} + \frac{5}{q} + 6 = 0$

Step 3

Combine the numerators over the common denominator.

$\frac{q \cdot q + 5}{q} + 6 = 0$

Step 4

Multiply $q$ by $q$ .

$\frac{q^{2} + 5}{q} + 6 = 0$

Step 5

To write $6$ as a fraction with a common denominator, multiply by $\frac{q}{q}$ .

$\frac{q^{2} + 5}{q} + \frac{6 q}{q} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{q^{2} + 5 + 6 q}{q} = 0$

Step 7

Factor $q^{2} + 5 + 6 q$ using the AC method.

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 $5$ and whose sum is $6$ .

$1, 5$

Write the factored form using these integers.

$\frac{(q + 1) (q + 5)}{q} = 0$

Step 8

Set the numerator equal to zero.

$(q + 1) (q + 5) = 0$

Step 9

Solve the equation for $q$ .

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

$q + 1 = 0$

$q + 5 = 0$

Set $q + 1$ equal to $0$ and solve for $q$ .

Set $q + 1$ equal to $0$ .

$q + 1 = 0$

Subtract $1$ from both sides of the equation.

$q = - 1$

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

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

$q + 5 = 0$

Subtract $5$ from both sides of the equation.

$q = - 5$

The final solution is all the values that make $(q + 1) (q + 5) = 0$ true.

$q = - 1, - 5$

Solve by Factoring q+5/q=-6

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