Algebra Examples

$2 x + x^{2} = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$2 u + u^{2} = 0$

Step 1.2

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

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Step 1.2.1

Factor $u$ out of $2 u$ .

$u \cdot 2 + u^{2} = 0$

Step 1.2.2

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

$u \cdot 2 + u \cdot u = 0$

Step 1.2.3

Factor $u$ out of $u \cdot 2 + u \cdot u$ .

$u (2 + u) = 0$

Step 1.3

Replace all occurrences of $u$ with $x$ .

$x (2 + x) = 0$

Step 2

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

$x = 0$

$2 + x = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $2 + x$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $2 + x$ equal to $0$ .

$2 + x = 0$

Step 4.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 5

The final solution is all the values that make $x (2 + x) = 0$ true.

$x = 0, - 2$