# Solve for x 3x^(2/3)+x^(1/3)-2=0

Factor the left side of the equation.
Rewrite as .
Let . Substitute for all occurrences of .
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Multiply by .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Replace all occurrences of with .
Replace the left side with the factored expression.
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 and solve.
Set the first factor equal to .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Simplify .
Cancel the common factor.
Divide by .
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Simplify .
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Raise to the power of .
The final solution is all the values that make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for x 3x^(2/3)+x^(1/3)-2=0