Solve by Factoring (x-3)^(2/3)+(x-3)^(1/3)-6=0

Math
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
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.
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Set the first factor equal to .
Add to both sides of the equation.
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Solve the equation for .
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Raise to the power of .
Move all terms not containing to the right side of the equation.
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Add to both sides of the equation.
Add and .
Set the next factor equal to and solve.
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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.
Solve the equation for .
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Raise to the power of .
Move all terms not containing to the right side of the equation.
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Add to both sides of the equation.
Add and .
The final solution is all the values that make true.
Solve by Factoring (x-3)^(2/3)+(x-3)^(1/3)-6=0

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