What is the synthetic method for solving higher order equations of one variable? Such as the title

What is the synthetic method for solving higher order equations of one variable? Such as the title

It is to extract the common factor and then merge it into the form of high-order x equation = 0
Then, according to the formula of each bracket after merging, the solution is carried out
For example, the decomposition of x ^ 3 + 3x ^ 2 + 3x + 1 = 0 is (x + 1) (x + 1) (x + 1) = 0, so x has three equal roots, x = - 1

It is known that the equation (m-1) x & # 178; - MX = 3 about X. when x = what, the equation is one variable linear equation

m=1
When m = 1, (m-1) x & # 178; = 0
The original equation is - 1 x = 3

Given the equation (M + 1) x + (m-1) = 0, when m takes (), it is a bivariate linear equation; when m takes (), it is a univariate linear equation
Sorry, the title is wrong, the known equation (M + 1) x + (m-1) y = 0, when m takes (), it is a bivariate linear equation; when m takes (), it is a univariate linear equation

Given the equation (M + 1) x + (m-1) = 0, when m takes (not equal to plus or minus 1), it is a quadratic equation of two variables; when m takes (equal to 1; or equal to - 1), it is a quadratic equation of one variable