Solve 8y^2+3y

$$8 y ^ { 2 } + 3 y$$

Factor

$$y\left(8y+3\right)$$

Solution Steps

Factor out y.

$$y\left(8y+3\right)$$

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.

$$8y^{2}+3y=0$$

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.

$$y=\frac{-3±\sqrt{3^{2}}}{2\times 8}$$

Take the square root of 3^{2}.

$$y=\frac{-3±3}{2\times 8}$$

Multiply 2 times 8.

$$y=\frac{-3±3}{16}$$

Now solve the equation y=\frac{-3±3}{16} when ± is plus. Add -3 to 3.

$$y=\frac{0}{16}$$

Divide 0 by 16.

$$y=0$$

Now solve the equation y=\frac{-3±3}{16} when ± is minus. Subtract 3 from -3.

$$y=-\frac{6}{16}$$

Reduce the fraction \frac{-6}{16} to lowest terms by extracting and canceling out 2.

$$y=-\frac{3}{8}$$

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{3}{8} for x_{2}.

$$8y^{2}+3y=8y\left(y-\left(-\frac{3}{8}\right)\right)$$

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

$$8y^{2}+3y=8y\left(y+\frac{3}{8}\right)$$

Add \frac{3}{8} to y by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$8y^{2}+3y=8y\times \frac{8y+3}{8}$$

Cancel out 8, the greatest common factor in 8 and 8.

$$8y^{2}+3y=y\left(8y+3\right)$$

Evaluate

$$y\left(8y+3\right)$$