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n\left(n-2\right)
Factor out n.
n^{2}-2n=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.
n=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{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.
n=\frac{-\left(-2\right)±2}{2}
Take the square root of \left(-2\right)^{2}.
n=\frac{2±2}{2}
The opposite of -2 is 2.
n=\frac{4}{2}
Now solve the equation n=\frac{2±2}{2} when ± is plus. Add 2 to 2.
n=2
Divide 4 by 2.
n=\frac{0}{2}
Now solve the equation n=\frac{2±2}{2} when ± is minus. Subtract 2 from 2.
n=0
Divide 0 by 2.
n^{2}-2n=\left(n-2\right)n
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 2 for x_{1} and 0 for x_{2}.