Solve -n^2+24n

$$- n ^ { 2 } + 24 n$$

Factor

$$n\left(24-n\right)$$

Solution Steps

Factor out n.

$$n\left(-n+24\right)$$

Steps Using the Quadratic Formula

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.

$$-n^{2}+24n=0$$

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.

$$n=\frac{-24±\sqrt{24^{2}}}{2\left(-1\right)}$$

Take the square root of 24^{2}.

$$n=\frac{-24±24}{2\left(-1\right)}$$

Multiply 2 times -1.

$$n=\frac{-24±24}{-2}$$

Now solve the equation n=\frac{-24±24}{-2} when ± is plus. Add -24 to 24.

$$n=\frac{0}{-2}$$

Divide 0 by -2.

$$n=0$$

Now solve the equation n=\frac{-24±24}{-2} when ± is minus. Subtract 24 from -24.

$$n=-\frac{48}{-2}$$

Divide -48 by -2.

$$n=24$$

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 24 for x_{2}.

$$-n^{2}+24n=-n\left(n-24\right)$$

Evaluate

$$n\left(24-n\right)$$