Algebra Examples

Solve: $q^{2} + q = 0$

Step 1

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

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Step 1.1

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

$q \cdot q + q = 0$

Step 1.2

Raise $q$ to the power of $1$ .

$q \cdot q + q = 0$

Step 1.3

Factor $q$ out of $q^{1}$ .

$q \cdot q + q \cdot 1 = 0$

Step 1.4

Factor $q$ out of $q \cdot q + q \cdot 1$ .

$q (q + 1) = 0$

Step 2

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

$q = 0$

$q + 1 = 0$

Step 3

Set $q$ equal to $0$ .

$q = 0$

Step 4

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

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Step 4.1

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

$q + 1 = 0$

Step 4.2

Subtract $1$ from both sides of the equation.

$q = - 1$

Step 5

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

$q = 0, - 1$