Solve r^2+6r

$$r ^ { 2 } + 6 r$$

Factor

$$r\left(r+6\right)$$

Solution Steps

Factor out r.

$$r\left(r+6\right)$$

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.

$$r^{2}+6r=0$$

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.

$$r=\frac{-6±\sqrt{6^{2}}}{2}$$

Take the square root of 6^{2}.

$$r=\frac{-6±6}{2}$$

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

$$r=\frac{0}{2}$$

Divide 0 by 2.

$$r=0$$

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

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

Divide -12 by 2.

$$r=-6$$

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 -6 for x_{2}.

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

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

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

Evaluate

$$r\left(r+6\right)$$