Algebra Examples

$a^{2} + a = 0$

Step 1

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

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Step 1.1

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

$a \cdot a + a = 0$

Step 1.2

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

$a \cdot a + a = 0$

Step 1.3

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

$a \cdot a + a \cdot 1 = 0$

Step 1.4

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

$a (a + 1) = 0$

Step 2

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

$a = 0$

$a + 1 = 0$

Step 3

Set $a$ equal to $0$ .

$a = 0$

Step 4

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

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Step 4.1

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

$a + 1 = 0$

Step 4.2

Subtract $1$ from both sides of the equation.

$a = - 1$

Step 5

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

$a = 0, - 1$