Solve 3a^2-21a

$$3 a ^ { 2 } - 21 a$$

Factor

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

Solution Steps

Factor out 3.

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

Consider a^{2}-7a. Factor out a.

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

Rewrite the complete factored expression.

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

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.

$$3a^{2}-21a=0$$

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.

$$a=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}}}{2\times 3}$$

Take the square root of \left(-21\right)^{2}.

$$a=\frac{-\left(-21\right)±21}{2\times 3}$$

The opposite of -21 is 21.

$$a=\frac{21±21}{2\times 3}$$

Multiply 2 times 3.

$$a=\frac{21±21}{6}$$

Now solve the equation a=\frac{21±21}{6} when ± is plus. Add 21 to 21.

$$a=\frac{42}{6}$$

Divide 42 by 6.

$$a=7$$

Now solve the equation a=\frac{21±21}{6} when ± is minus. Subtract 21 from 21.

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

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 7 for x_{1} and 0 for x_{2}.

$$3a^{2}-21a=3\left(a-7\right)a$$

Evaluate

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