Solve for q q^3-q^2-30q=0

$q^{3} - q^{2} - 30 q = 0$

Factor the left side of the equation.

Factor $q$ out of $q^{3} - q^{2} - 30 q$ .

Factor $q$ out of $q^{3}$ .

$q \cdot q^{2} - q^{2} - 30 q = 0$

Factor $q$ out of $- q^{2}$ .

$q \cdot q^{2} + q (- q) - 30 q = 0$

Factor $q$ out of $- 30 q$ .

$q \cdot q^{2} + q (- q) + q \cdot - 30 = 0$

Factor $q$ out of $q \cdot q^{2} + q (- q)$ .

$q (q^{2} - q) + q \cdot - 30 = 0$

Factor $q$ out of $q (q^{2} - q) + q \cdot - 30$ .

$q (q^{2} - q - 30) = 0$

Factor.

Factor $q^{2} - q - 30$ 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 $- 30$ and whose sum is $- 1$ .

$- 6, 5$

Write the factored form using these integers.

$q ((q - 6) (q + 5)) = 0$

Remove unnecessary parentheses.

$q (q - 6) (q + 5) = 0$

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

$q = 0$

$q - 6 = 0$

$q + 5 = 0$

Set $q$ equal to $0$ .

$q = 0$

Set $q - 6$ equal to $0$ and solve for $q$ .

Set $q - 6$ equal to $0$ .

$q - 6 = 0$

Add $6$ to both sides of the equation.

$q = 6$

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 $q (q - 6) (q + 5) = 0$ true.

$q = 0, 6, - 5$

Solve for q q^3-q^2-30q=0

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