Solve 6a^2-15a

$$6 a ^ { 2 } - 15 a$$

Factor

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

Solution Steps

Factor out 3.

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

Consider 2a^{2}-5a. Factor out a.

$$a\left(2a-5\right)$$

Rewrite the complete factored expression.

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

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.

$$6a^{2}-15a=0$$

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.

$$a=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}}}{2\times 6}$$

Take the square root of \left(-15\right)^{2}.

$$a=\frac{-\left(-15\right)±15}{2\times 6}$$

The opposite of -15 is 15.

$$a=\frac{15±15}{2\times 6}$$

Multiply 2 times 6.

$$a=\frac{15±15}{12}$$

Now solve the equation a=\frac{15±15}{12} when ± is plus. Add 15 to 15.

$$a=\frac{30}{12}$$

Reduce the fraction \frac{30}{12} to lowest terms by extracting and canceling out 6.

$$a=\frac{5}{2}$$

Now solve the equation a=\frac{15±15}{12} when ± is minus. Subtract 15 from 15.

$$a=\frac{0}{12}$$

Divide 0 by 12.

$$a=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5}{2} for x_{1} and 0 for x_{2}.

$$6a^{2}-15a=6\left(a-\frac{5}{2}\right)a$$

Subtract \frac{5}{2} from a by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$6a^{2}-15a=6\times \frac{2a-5}{2}a$$

Cancel out 2, the greatest common factor in 6 and 2.

$$6a^{2}-15a=3\left(2a-5\right)a$$

Evaluate

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