Algebra Examples

$x^{2} e^{x} + 2 x e^{x}$

Step 1

Set $x^{2} e^{x} + 2 x e^{x}$ equal to $0$ .

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

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Factor $x e^{x}$ out of $x^{2} e^{x} + 2 x e^{x}$ .

Tap for more steps...

Step 2.1.1

Factor $x e^{x}$ out of $x^{2} e^{x}$ .

$x e^{x} (x) + 2 x e^{x} = 0$

Step 2.1.2

Factor $x e^{x}$ out of $2 x e^{x}$ .

$x e^{x} (x) + x e^{x} (2) = 0$

Step 2.1.3

Factor $x e^{x}$ out of $x e^{x} (x) + x e^{x} (2)$ .

$x e^{x} (x + 2) = 0$

Step 2.2

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

$x = 0$

$e^{x} = 0$

$x + 2 = 0$

Step 2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.4

Set $e^{x}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.4.1

Set $e^{x}$ equal to $0$ .

$e^{x} = 0$

Step 2.4.2

Solve $e^{x} = 0$ for $x$ .

Tap for more steps...

Step 2.4.2.1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{x}) = \ln (0)$

Step 2.4.2.2

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 2.4.2.3

There is no solution for $e^{x} = 0$

No solution

Step 2.5

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

Tap for more steps...

Step 2.5.1

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

$x + 2 = 0$

Step 2.5.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 2.6

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

$x = 0, - 2$

Step 3