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5\left(x^{2}+5x\right)
Factor out 5.
x\left(x+5\right)
Consider x^{2}+5x. Factor out x.
5x\left(x+5\right)
Rewrite the complete factored expression.
5x^{2}+25x=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{-25±\sqrt{25^{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.
x=\frac{-25±25}{2\times 5}
Take the square root of 25^{2}.
x=\frac{-25±25}{10}
Multiply 2 times 5.
x=\frac{0}{10}
Now solve the equation x=\frac{-25±25}{10} when ± is plus. Add -25 to 25.
x=0
Divide 0 by 10.
x=-\frac{50}{10}
Now solve the equation x=\frac{-25±25}{10} when ± is minus. Subtract 25 from -25.
x=-5
Divide -50 by 10.
5x^{2}+25x=5x\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}.
5x^{2}+25x=5x\left(x+5\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.