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7\left(-a^{2}+3a\right)
Factor out 7.
a\left(-a+3\right)
Consider -a^{2}+3a. Factor out a.
7a\left(-a+3\right)
Rewrite the complete factored expression.
-7a^{2}+21a=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.
a=\frac{-21±\sqrt{21^{2}}}{2\left(-7\right)}
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.
a=\frac{-21±21}{2\left(-7\right)}
Take the square root of 21^{2}.
a=\frac{-21±21}{-14}
Multiply 2 times -7.
a=\frac{0}{-14}
Now solve the equation a=\frac{-21±21}{-14} when ± is plus. Add -21 to 21.
a=0
Divide 0 by -14.
a=-\frac{42}{-14}
Now solve the equation a=\frac{-21±21}{-14} when ± is minus. Subtract 21 from -21.
a=3
Divide -42 by -14.
-7a^{2}+21a=-7a\left(a-3\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 3 for x_{2}.