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10\left(x^{2}+5x\right)
Factor out 10.
x\left(x+5\right)
Consider x^{2}+5x. Factor out x.
10x\left(x+5\right)
Rewrite the complete factored expression.
10x^{2}+50x=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{-50±\sqrt{50^{2}}}{2\times 10}
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{-50±50}{2\times 10}
Take the square root of 50^{2}.
x=\frac{-50±50}{20}
Multiply 2 times 10.
x=\frac{0}{20}
Now solve the equation x=\frac{-50±50}{20} when ± is plus. Add -50 to 50.
x=0
Divide 0 by 20.
x=-\frac{100}{20}
Now solve the equation x=\frac{-50±50}{20} when ± is minus. Subtract 50 from -50.
x=-5
Divide -100 by 20.
10x^{2}+50x=10x\left(x-\left(-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 -5 for x_{2}.
10x^{2}+50x=10x\left(x+5\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.