Chapter 4.7, Problem 15WE

To determine

To solve: the function and identify all double zeroes

Answer to Problem 15WE

The value of $2y^2+y=6$ is $y=\left\{-2,\frac{3}{2}\right\}$

Explanation of Solution

Given information: The function is $2y^2+y=6$

Calculation:

  $\begin{array}{l}2y^2+y=6\\ 2y^2+4y-3y-6=0\\ 2y\left(y+2\right)-3\left(y+2\right)=0\\ \left(y+2\right)\left(2y-3\right)=0\end{array}$

The given equation already has $0$ as one side, and the other side is already factored

Simplify set each factor equal to $0$

  $\begin{array}{l}\left(y+2\right)\left(2y-3\right)=0\\ y+2=0\\ y=-2\\ 2y-3=0\\ 2y=3\\ y=\frac{3}{2}\\ y=\left\{-2,\frac{3}{2}\right\}\end{array}$