# Solve for x x^6-124x^3-125=0

Factor the left side of the equation.
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
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 .
Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
Move to the left of .
Raise to the power of .
Rewrite as .
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Factor.
Simplify.
Multiply by .
One to any power is one.
Remove unnecessary parentheses.
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.
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 .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Move to the left of .
Multiply by .
Factor out of .
Multiply by .
Multiply by .
The final answer is the combination of both solutions.
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from 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 .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Multiply by .
The final answer is the combination of both solutions.
The final solution is all the values that make true.
Solve for x x^6-124x^3-125=0