solving a 6-term quintic equation

We will solve an awesome quintic equation x^5+x^4+x^3+x^2+x+1=0 via factor by grouping. Notice that this quintic expression has 6 terms. After factoring, we will then be able to solve a quadratic equation by using the quadratic formula and a cubic equation by factoring out the sum of two cubes.

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"Just Algebra" (by blackpenredpen) is dedicated to helping middle school, high school, and community college students who need to learn algebra. Topics include how to solve various equations (linear equations, quadratic equations, square root equations, rational equations, exponential equations, logarithmic equations, and more), factoring techniques, word problems, functions, graphs, Pythagorean Theorem, and more. We will also cover standardized test problems such as the SAT. Free feel to leave your questions in the comment!
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