Solve for all values of xx by factoring.

x, squared, plus, 4, x, equals, 0
x
2
+4x=
0

1 answer

To solve the equation \(x^2 + 4x = 0\) by factoring, follow these steps:

  1. Factor out the common term. The common term here is \(x\):

    \[ x(x + 4) = 0 \]

  2. Set each factor to zero. This gives us two equations to solve:

    \[ x = 0 \]

    and

    \[ x + 4 = 0 \]

    Solving the second equation:

    \[ x = -4 \]

  3. Combine the solutions. The solutions to the original equation are:

    \[ x = 0 \quad \text{and} \quad x = -4 \]

Therefore, the final answers are:

\[ x = 0 \quad \text{and} \quad x = -4 \]