# Find All Complex Solutions x^4+2x^3-4x^2+x=0

Factor the left side of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Raise to the power of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor.
Factor using the rational roots test.
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Substitute into the polynomial.
Raise to the power of .
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Divide by .
Write as a set of factors.
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to .
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
Set the next factor equal to .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Multiply by .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Multiply by .
Change the to .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Multiply by .
Change the to .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
The final answer is the combination of both solutions.
The final solution is all the values that make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Find All Complex Solutions x^4+2x^3-4x^2+x=0