The solution of the equation
is 
Further explanation:
The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is
.

The polynomial function has n roots or zeroes.
Given:
The equation is 
Explanation:
The equation
is a quadratic equation and has 2 solutions or zeros.
Solve the equation 

Further solve the above equation using middle term splitting.
![\begin{aligned}6{\left( {2x + 4} \right)^2} - \left( {2x + 4} \right) - 2 &= 0 \hfill\\6{\left( {2x + 4} \right)^2} - 4\left( {2x + 4} \right) + 3\left( {2x + 4} \right) - 2 &= 0 \hfill\\3\left( {2x + 4} \right)\left[ {2\left( {2x + 4} \right) + 1} \right] - 2\left[ {2\left( {2x + 4} \right) + 1} \right] &= 0 \hfill\\\left[ {2\left( {2x + 4} \right) + 1} \right]\left[ {3\left( {2x + 4} \right) - 2} \right] &= 0 \hfill\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D6%7B%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%5E2%7D%20-%20%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%20-%202%20%26%3D%200%20%5Chfill%5C%5C6%7B%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%5E2%7D%20-%204%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%20%2B%203%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%20-%202%20%26%3D%200%20%5Chfill%5C%5C3%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%5Cleft%5B%20%7B2%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%20%2B%201%7D%20%5Cright%5D%20-%202%5Cleft%5B%20%7B2%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%20%2B%201%7D%20%5Cright%5D%20%26%3D%200%20%5Chfill%5C%5C%5Cleft%5B%20%7B2%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%20%2B%201%7D%20%5Cright%5D%5Cleft%5B%20%7B3%5Cleft%28%20%7B2x%20%2B%204%7D%20%5Cright%29%20-%202%7D%20%5Cright%5D%20%26%3D%200%20%5Chfill%5C%5C%5Cend%7Baligned%7D)
Again solve the above equation.

The solution of the equation
is 
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Quadratic equation
Keywords: roots, linear equation, quadratic equation, zeros, function, polynomial, solution, cubic function, degree of the function.