Solve 14c^2-9c

$$14 c ^ { 2 } - 9 c$$

Factor

$$c\left(14c-9\right)$$

Solution Steps

Factor out c.

$$c\left(14c-9\right)$$

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.

$$14c^{2}-9c=0$$

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.

$$c=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2\times 14}$$

Take the square root of \left(-9\right)^{2}.

$$c=\frac{-\left(-9\right)±9}{2\times 14}$$

The opposite of -9 is 9.

$$c=\frac{9±9}{2\times 14}$$

Multiply 2 times 14.

$$c=\frac{9±9}{28}$$

Now solve the equation c=\frac{9±9}{28} when ± is plus. Add 9 to 9.

$$c=\frac{18}{28}$$

Reduce the fraction \frac{18}{28} to lowest terms by extracting and canceling out 2.

$$c=\frac{9}{14}$$

Now solve the equation c=\frac{9±9}{28} when ± is minus. Subtract 9 from 9.

$$c=\frac{0}{28}$$

Divide 0 by 28.

$$c=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{9}{14} for x_{1} and 0 for x_{2}.

$$14c^{2}-9c=14\left(c-\frac{9}{14}\right)c$$

Subtract \frac{9}{14} from c by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$14c^{2}-9c=14\times \frac{14c-9}{14}c$$

Cancel out 14, the greatest common factor in 14 and 14.

$$14c^{2}-9c=\left(14c-9\right)c$$

Evaluate

$$c\left(14c-9\right)$$