Solve 9c^2+36c

$$9 c ^ { 2 } + 36 c$$

Factor

$$9c\left(c+4\right)$$

Solution Steps

Factor out 9.

$$9\left(c^{2}+4c\right)$$

Consider c^{2}+4c. Factor out c.

$$c\left(c+4\right)$$

Rewrite the complete factored expression.

$$9c\left(c+4\right)$$

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.

$$9c^{2}+36c=0$$

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.

$$c=\frac{-36±\sqrt{36^{2}}}{2\times 9}$$

Take the square root of 36^{2}.

$$c=\frac{-36±36}{2\times 9}$$

Multiply 2 times 9.

$$c=\frac{-36±36}{18}$$

Now solve the equation c=\frac{-36±36}{18} when ± is plus. Add -36 to 36.

$$c=\frac{0}{18}$$

Divide 0 by 18.

$$c=0$$

Now solve the equation c=\frac{-36±36}{18} when ± is minus. Subtract 36 from -36.

$$c=-\frac{72}{18}$$

Divide -72 by 18.

$$c=-4$$

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 -4 for x_{2}.

$$9c^{2}+36c=9c\left(c-\left(-4\right)\right)$$

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

$$9c^{2}+36c=9c\left(c+4\right)$$

Evaluate

$$9c\left(c+4\right)$$