Solve 3y^2+2y

$$3 y ^ { 2 } + 2 y$$

Factor

$$y\left(3y+2\right)$$

Solution Steps

Factor out y.

$$y\left(3y+2\right)$$

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.

$$3y^{2}+2y=0$$

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.

$$y=\frac{-2±\sqrt{2^{2}}}{2\times 3}$$

Take the square root of 2^{2}.

$$y=\frac{-2±2}{2\times 3}$$

Multiply 2 times 3.

$$y=\frac{-2±2}{6}$$

Now solve the equation y=\frac{-2±2}{6} when ± is plus. Add -2 to 2.

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

Divide 0 by 6.

$$y=0$$

Now solve the equation y=\frac{-2±2}{6} when ± is minus. Subtract 2 from -2.

$$y=-\frac{4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$y=-\frac{2}{3}$$

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{2}{3} for x_{2}.

$$3y^{2}+2y=3y\left(y-\left(-\frac{2}{3}\right)\right)$$

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

$$3y^{2}+2y=3y\left(y+\frac{2}{3}\right)$$

Add \frac{2}{3} to y by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$3y^{2}+2y=3y\times \frac{3y+2}{3}$$

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

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

Evaluate

$$y\left(3y+2\right)$$