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Question: How do you solve \(3t(t + 5) - {t^2} = 2{t^2} + 4t - 1\)?...

How do you solve 3t(t+5)−t2=2t2+4t−13t(t + 5) - {t^2} = 2{t^2} + 4t - 1?

Explanation

Solution

According to given in the question we have to determine the value of the given polynomial equation which is 3t(t+5)−t2=2t2+4t−13t(t + 5) - {t^2} = 2{t^2} + 4t - 1. So, first of all we have to open the smaller bracket in the left hand side of the given expression and then we have to multiply the terms which can be easily multiplied.
Now, we have to eliminate the terms which can be eliminated by adding or subtracting the terms so that we can simplify the expression.
Now, to eliminate the remaining terms we have to arrange the term in any one of the sides which can be either left hand side or the right hand side.
Now, again we have to eliminate and add the terms by subtracting and adding the terms which can be eliminated or added.

Complete step-by-step answer:
Step 1: First of all we have to open the smaller bracket in the left hand side of the given expression and then we have to multiply the terms which can be easily multiplied as mentioned in the solution hint. Hence,
⇒3t2+15t−t2=2t2+4t−1 ⇒2t2+15t=2t2+4t−1  \Rightarrow 3{t^2} + 15t - {t^2} = 2{t^2} + 4t - 1 \\\ \Rightarrow 2{t^2} + 15t = 2{t^2} + 4t - 1 \\\
Step 2: Now, to eliminate the remaining terms we have to arrange the term in any one of the sides which can be either the left hand side or the right hand side. Hence,
⇒2t2−2t2+15t−4t=−1\Rightarrow 2{t^2} - 2{t^2} + 15t - 4t = - 1
Step 3: Now, again we have to eliminate and add the terms by subtracting and adding the terms which can be eliminated or added. Hence,
⇒11t=−1 ⇒t=−111  \Rightarrow 11t = - 1 \\\ \Rightarrow t = - \dfrac{1}{{11}} \\\

Final solution: Hence, with the help of eliminating and adding the terms we have determined the solution of the expression 3t(t+5)−t2=2t2+4t−13t(t + 5) - {t^2} = 2{t^2} + 4t - 1 given is ⇒t=−111 \Rightarrow t = - \dfrac{1}{{11}}.

Note:
To determine the required value of t it is necessary that we have to open all the brackets and then we have to add or eliminate the terms by adding and subtracting them.
In the case of variables we can’t add or subtract different types of variables such as we can’t add or subtract if one of the variable is a2{a^2} and if the other variable is b,b2b,{b^2} or a3{a^3}.