Chapter 4.5, Problem 31WE

To determine

To simplify the equation

  $y\left(2-3y\right)+3\left(y^2-4\right)=0$

Answer to Problem 31WE

  $y=6$

Explanation of Solution

Given:

  $y\left(2-3y\right)+3\left(y^2-4\right)=0$

Concept Used:

• To simplify an expression first use distributive property to remove any grouping symbol, and then add/subtract like terms.
• Distributive property: $a\left(b\pm c\right)=ab\pm ac$
• If an expression contains more than one operations between its terms and brackets, first solve the terms inside brackets and then apply division followed by multiplication, addition and subtraction.

Calculation:

To simplify the equation

  $y\left(2-3y\right)+3\left(y^2-4\right)=0$

First use distributive property to remove any grouping symbol as,

  $\begin{array}{l}y\left(2-3y\right)+3\left(y^2-4\right)=0\\ \Rightarrow y\left(2\right)+y\left(-3y\right)+3\left(y^2\right)+3\left(-4\right)=0\\ \Rightarrow 2y-3y^2+3y^2-12=0\\ \Rightarrow 2y-12=0\end{array}$

Now, add $12$ on both sides of the equation as,

  $\begin{array}{l}2y-12+12=0+12\\ \Rightarrow 2y=12\end{array}$

Now divide both sides of the equation by $2$ as

  $\begin{array}{l}\frac{2y}{2}=\frac{12}{2}\\ \Rightarrow y=6\end{array}$

Thus, the simplified equation becomes

  $y=6$