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7\left(2x^{2}-x\right)
Factor out 7.
x\left(2x-1\right)
Consider 2x^{2}-x. Factor out x.
7x\left(2x-1\right)
Rewrite the complete factored expression.
14x^{2}-7x=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{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2\times 14}
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{-\left(-7\right)±7}{2\times 14}
Take the square root of \left(-7\right)^{2}.
x=\frac{7±7}{2\times 14}
The opposite of -7 is 7.
x=\frac{7±7}{28}
Multiply 2 times 14.
x=\frac{14}{28}
Now solve the equation x=\frac{7±7}{28} when ± is plus. Add 7 to 7.
x=\frac{1}{2}
Reduce the fraction \frac{14}{28} to lowest terms by extracting and canceling out 14.
x=\frac{0}{28}
Now solve the equation x=\frac{7±7}{28} when ± is minus. Subtract 7 from 7.
x=0
Divide 0 by 28.
14x^{2}-7x=14\left(x-\frac{1}{2}\right)x
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{2} for x_{1} and 0 for x_{2}.
14x^{2}-7x=14\times \frac{2x-1}{2}x
Subtract \frac{1}{2} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.
14x^{2}-7x=7\left(2x-1\right)x
Cancel out 2, the greatest common factor in 14 and 2.