Solve 3a^2-7a

$$3 a ^ { 2 } - 7 a$$

Factor

$$a\left(3a-7\right)$$

Solution Steps

Factor out a.

$$a\left(3a-7\right)$$

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.

$$3a^{2}-7a=0$$

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.

$$a=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2\times 3}$$

Take the square root of \left(-7\right)^{2}.

$$a=\frac{-\left(-7\right)±7}{2\times 3}$$

The opposite of -7 is 7.

$$a=\frac{7±7}{2\times 3}$$

Multiply 2 times 3.

$$a=\frac{7±7}{6}$$

Now solve the equation a=\frac{7±7}{6} when ± is plus. Add 7 to 7.

$$a=\frac{14}{6}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$a=\frac{7}{3}$$

Now solve the equation a=\frac{7±7}{6} when ± is minus. Subtract 7 from 7.

$$a=\frac{0}{6}$$

Divide 0 by 6.

$$a=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{7}{3} for x_{1} and 0 for x_{2}.

$$3a^{2}-7a=3\left(a-\frac{7}{3}\right)a$$

Subtract \frac{7}{3} from a by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$3a^{2}-7a=3\times \frac{3a-7}{3}a$$

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

$$3a^{2}-7a=\left(3a-7\right)a$$

Evaluate

$$a\left(3a-7\right)$$