Solve 6a^2+2a

$$6 a ^ { 2 } + 2 a$$

Factor

$$2a\left(3a+1\right)$$

Solution Steps

Factor out 2.

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

Consider 3a^{2}+a. Factor out a.

$$a\left(3a+1\right)$$

Rewrite the complete factored expression.

$$2a\left(3a+1\right)$$

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.

$$6a^{2}+2a=0$$

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.

$$a=\frac{-2±\sqrt{2^{2}}}{2\times 6}$$

Take the square root of 2^{2}.

$$a=\frac{-2±2}{2\times 6}$$

Multiply 2 times 6.

$$a=\frac{-2±2}{12}$$

Now solve the equation a=\frac{-2±2}{12} when ± is plus. Add -2 to 2.

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

Divide 0 by 12.

$$a=0$$

Now solve the equation a=\frac{-2±2}{12} when ± is minus. Subtract 2 from -2.

$$a=-\frac{4}{12}$$

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

$$a=-\frac{1}{3}$$

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

$$6a^{2}+2a=6a\left(a-\left(-\frac{1}{3}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$6a^{2}+2a=6a\left(a+\frac{1}{3}\right)$$

Add \frac{1}{3} to a by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$6a^{2}+2a=6a\times \frac{3a+1}{3}$$

Cancel out 3, the greatest common factor in 6 and 3.

$$6a^{2}+2a=2a\left(3a+1\right)$$

Evaluate

$$2a\left(3a+1\right)$$