First we need to factor trinomial $ \color{blue}{ x^2+x } $ and than we use factored form to solve an equation $ \color{blue}{ x^2+x = 0} $.

Step 1: Factor $ x $ out of $ x^{2}+x $ :

$$ x^{2}+x = x \cdot( x+1 ) $$

Step 2: Set each factor to zero and solve equations.

$$ \begin{array}{ccc} \begin{aligned} x &= 0 \\ ~ & ~ \end{aligned} & ~ & \begin{aligned} x+1 &= 0 \\ x &= -1 \end{aligned} \end{array} $$

Quadratic Equation Solver