Rewrite as .

Let . Substitute for all occurrences of .

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 .

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 .

Raise to the power of .

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Add and .

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 .

Raise to the power of .

Move all terms not containing to the right side of the equation.

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)-12=0