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 .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

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 .

Subtract from both sides of the equation.

Set the next factor equal to .

Add to both sides of the equation.

Set the next factor equal to .

Subtract from both sides of the equation.

Set the next factor equal to .

Add to both sides of the equation.

The final solution is all the values that make true.

Solve by Factoring z^4-65z^2+64=0