Solve for q q+4/q=-5

$q + \frac{4}{q} = - 5$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, q, 1$

The LCM of one and any expression is the expression.

$q$

Multiply each term in $q + \frac{4}{q} = - 5$ by $q$ to eliminate the fractions.

Multiply each term in $q + \frac{4}{q} = - 5$ by $q$ .

$q \cdot q + \frac{4}{q} q = - 5 q$

Simplify the left side.

Simplify each term.

Multiply $q$ by $q$ .

$q^{2} + \frac{4}{q} q = - 5 q$

Cancel the common factor of $q$ .

Cancel the common factor.

$q^{2} + \frac{4}{q} q = - 5 q$

Rewrite the expression.

$q^{2} + 4 = - 5 q$

Solve the equation.

Add $5 q$ to both sides of the equation.

$q^{2} + 4 + 5 q = 0$

Factor $q^{2} + 4 + 5 q$ 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 $4$ and whose sum is $5$ .

$1, 4$

Write the factored form using these integers.

$(q + 1) (q + 4) = 0$

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

$q + 1 = 0$

$q + 4 = 0$

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 $q + 4$ equal to $0$ and solve for $q$ .

Set $q + 4$ equal to $0$ .

$q + 4 = 0$

Subtract $4$ from both sides of the equation.

$q = - 4$

The final solution is all the values that make $(q + 1) (q + 4) = 0$ true.

$q = - 1, - 4$

Solve for q q+4/q=-5

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