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w\left(5w+1\right)
Factor out w.
5w^{2}+w=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.
w=\frac{-1±\sqrt{1^{2}}}{2\times 5}
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.
w=\frac{-1±1}{2\times 5}
Take the square root of 1^{2}.
w=\frac{-1±1}{10}
Multiply 2 times 5.
w=\frac{0}{10}
Now solve the equation w=\frac{-1±1}{10} when ± is plus. Add -1 to 1.
w=0
Divide 0 by 10.
w=-\frac{2}{10}
Now solve the equation w=\frac{-1±1}{10} when ± is minus. Subtract 1 from -1.
w=-\frac{1}{5}
Reduce the fraction \frac{-2}{10} to lowest terms by extracting and canceling out 2.
5w^{2}+w=5w\left(w-\left(-\frac{1}{5}\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 -\frac{1}{5} for x_{2}.
5w^{2}+w=5w\left(w+\frac{1}{5}\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.
5w^{2}+w=5w\times \frac{5w+1}{5}
Add \frac{1}{5} to w by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
5w^{2}+w=w\left(5w+1\right)
Cancel out 5, the greatest common factor in 5 and 5.