Let's first expand the terms using the distributive property:
(6x^2 + x + 1)^2 - (3x^2 - x - 80)^2 = 0
Expanding the squares gives:
(36x^4 + 12x^3 + 12x^2 + x^2 + 2x + 1) - (9x^4 - 6x^3 - 240x^2 - 6x^3 + 4x^2 + 160x + x^2 - 80x - 80^2) = 0
Simplifying, we get:
27x^4 + 18x^3 + 28x^2 - 142x - 6399 = 0
So, the solution to the equation is:
Let's first expand the terms using the distributive property:
(6x^2 + x + 1)^2 - (3x^2 - x - 80)^2 = 0
Expanding the squares gives:
(36x^4 + 12x^3 + 12x^2 + x^2 + 2x + 1) - (9x^4 - 6x^3 - 240x^2 - 6x^3 + 4x^2 + 160x + x^2 - 80x - 80^2) = 0
Simplifying, we get:
27x^4 + 18x^3 + 28x^2 - 142x - 6399 = 0
So, the solution to the equation is:
27x^4 + 18x^3 + 28x^2 - 142x - 6399 = 0