Solve -6n-n^2

$$- 6 n - n ^ { 2 }$$

Factor

$$-n\left(n+6\right)$$

Solution Steps

Factor out n.

$$n\left(-6-n\right)$$

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.

$$-n^{2}-6n=0$$

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.

$$n=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\left(-1\right)}$$

Take the square root of \left(-6\right)^{2}.

$$n=\frac{-\left(-6\right)±6}{2\left(-1\right)}$$

The opposite of -6 is 6.

$$n=\frac{6±6}{2\left(-1\right)}$$

Multiply 2 times -1.

$$n=\frac{6±6}{-2}$$

Now solve the equation n=\frac{6±6}{-2} when ± is plus. Add 6 to 6.

$$n=\frac{12}{-2}$$

Divide 12 by -2.

$$n=-6$$

Now solve the equation n=\frac{6±6}{-2} when ± is minus. Subtract 6 from 6.

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

Divide 0 by -2.

$$n=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -6 for x_{1} and 0 for x_{2}.

$$-n^{2}-6n=-\left(n-\left(-6\right)\right)n$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$-n^{2}-6n=-\left(n+6\right)n$$

Evaluate

$$-n\left(n+6\right)$$