Solve 15c^2-10c

$$15 c ^ { 2 } - 10 c$$

Factor

$$5c\left(3c-2\right)$$

Solution Steps

Factor out 5.

$$5\left(3c^{2}-2c\right)$$

Consider 3c^{2}-2c. Factor out c.

$$c\left(3c-2\right)$$

Rewrite the complete factored expression.

$$5c\left(3c-2\right)$$

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.

$$15c^{2}-10c=0$$

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.

$$c=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\times 15}$$

Take the square root of \left(-10\right)^{2}.

$$c=\frac{-\left(-10\right)±10}{2\times 15}$$

The opposite of -10 is 10.

$$c=\frac{10±10}{2\times 15}$$

Multiply 2 times 15.

$$c=\frac{10±10}{30}$$

Now solve the equation c=\frac{10±10}{30} when ± is plus. Add 10 to 10.

$$c=\frac{20}{30}$$

Reduce the fraction \frac{20}{30} to lowest terms by extracting and canceling out 10.

$$c=\frac{2}{3}$$

Now solve the equation c=\frac{10±10}{30} when ± is minus. Subtract 10 from 10.

$$c=\frac{0}{30}$$

Divide 0 by 30.

$$c=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{2}{3} for x_{1} and 0 for x_{2}.

$$15c^{2}-10c=15\left(c-\frac{2}{3}\right)c$$

Subtract \frac{2}{3} from c by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$15c^{2}-10c=15\times \frac{3c-2}{3}c$$

Cancel out 3, the greatest common factor in 15 and 3.

$$15c^{2}-10c=5\left(3c-2\right)c$$

Evaluate

$$5c\left(3c-2\right)$$