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A\left(A-4\right)
Factor out A.
A^{2}-4A=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{-\left(-4\right)±\sqrt{\left(-4\right)^{2}}}{2}
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{-\left(-4\right)±4}{2}
Take the square root of \left(-4\right)^{2}.
A=\frac{4±4}{2}
The opposite of -4 is 4.
A=\frac{8}{2}
Now solve the equation A=\frac{4±4}{2} when ± is plus. Add 4 to 4.
A=4
Divide 8 by 2.
A=\frac{0}{2}
Now solve the equation A=\frac{4±4}{2} when ± is minus. Subtract 4 from 4.
A=0
Divide 0 by 2.
A^{2}-4A=\left(A-4\right)A
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 4 for x_{1} and 0 for x_{2}.