Chapter 4.7, Problem 23WE

To determine

To solve: the function and identify all double zeroes

Answer to Problem 23WE

The value of $3t\left(t+1\right)=4\left(t+1\right)$ is $t=\left\{-1,\frac{4}{3}\right\}$

Explanation of Solution

Given information: The function is $3t\left(t+1\right)=4\left(t+1\right)$

Calculation:

  $\begin{array}{l}3t\left(t+1\right)=4\left(t+1\right)\\ 3t\left(t+1\right)-4\left(t+1\right)=0\\ \left(t+1\right)\left(3t-4\right)=0\end{array}$

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

Simplify set each factor equal to $0$

  $\begin{array}{l}\left(t+1\right)\left(3t-4\right)=0\\ t+1=0\\ t=-1\\ 3t-4=0\\ 3t=4\\ t=\frac{4}{3}\\ t=\left\{-1,\frac{4}{3}\right\}\end{array}$