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x\left(x+2\right)
Factor out x.
x^{2}+2x=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-2±\sqrt{2^{2}}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-2±2}{2}
Take the square root of 2^{2}.
x=\frac{0}{2}
Now solve the equation x=\frac{-2±2}{2} when ± is plus. Add -2 to 2.
x=0
Divide 0 by 2.
x=\frac{-4}{2}
Now solve the equation x=\frac{-2±2}{2} when ± is minus. Subtract 2 from -2.
x=-2
Divide -4 by 2.
x^{2}+2x=x\left(x-\left(-2\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -2 for x_{2}.
x^{2}+2x=x\left(x+2\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.