Solve 15y^2+18y

$$15 y ^ { 2 } + 18 y$$

Factor

$$3y\left(5y+6\right)$$

Solution Steps

Factor out 3.

$$3\left(5y^{2}+6y\right)$$

Consider 5y^{2}+6y. Factor out y.

$$y\left(5y+6\right)$$

Rewrite the complete factored expression.

$$3y\left(5y+6\right)$$

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.

$$15y^{2}+18y=0$$

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.

$$y=\frac{-18±\sqrt{18^{2}}}{2\times 15}$$

Take the square root of 18^{2}.

$$y=\frac{-18±18}{2\times 15}$$

Multiply 2 times 15.

$$y=\frac{-18±18}{30}$$

Now solve the equation y=\frac{-18±18}{30} when ± is plus. Add -18 to 18.

$$y=\frac{0}{30}$$

Divide 0 by 30.

$$y=0$$

Now solve the equation y=\frac{-18±18}{30} when ± is minus. Subtract 18 from -18.

$$y=-\frac{36}{30}$$

Reduce the fraction \frac{-36}{30} to lowest terms by extracting and canceling out 6.

$$y=-\frac{6}{5}$$

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{6}{5} for x_{2}.

$$15y^{2}+18y=15y\left(y-\left(-\frac{6}{5}\right)\right)$$

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

$$15y^{2}+18y=15y\left(y+\frac{6}{5}\right)$$

Add \frac{6}{5} to y by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$15y^{2}+18y=15y\times \frac{5y+6}{5}$$

Cancel out 5, the greatest common factor in 15 and 5.

$$15y^{2}+18y=3y\left(5y+6\right)$$

Evaluate

$$3y\left(5y+6\right)$$