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2\left(9x^{2}+5x\right)
Factor out 2.
x\left(9x+5\right)
Consider 9x^{2}+5x. Factor out x.
2x\left(9x+5\right)
Rewrite the complete factored expression.
18x^{2}+10x=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{-10±\sqrt{10^{2}}}{2\times 18}
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{-10±10}{2\times 18}
Take the square root of 10^{2}.
x=\frac{-10±10}{36}
Multiply 2 times 18.
x=\frac{0}{36}
Now solve the equation x=\frac{-10±10}{36} when ± is plus. Add -10 to 10.
x=0
Divide 0 by 36.
x=-\frac{20}{36}
Now solve the equation x=\frac{-10±10}{36} when ± is minus. Subtract 10 from -10.
x=-\frac{5}{9}
Reduce the fraction \frac{-20}{36} to lowest terms by extracting and canceling out 4.
18x^{2}+10x=18x\left(x-\left(-\frac{5}{9}\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{5}{9} for x_{2}.
18x^{2}+10x=18x\left(x+\frac{5}{9}\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.
18x^{2}+10x=18x\times \frac{9x+5}{9}
Add \frac{5}{9} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
18x^{2}+10x=2x\left(9x+5\right)
Cancel out 9, the greatest common factor in 18 and 9.