Rewrite the absolute value equation as four equations without absolute value bars.

After simplifying, there are only two unique equations to be solved.

Move all terms containing to the left side of the equation.

Subtract from both sides of the equation.

Combine the opposite terms in .

Subtract from .

Add and .

Since , there are no solutions.

No solution

No solution

Simplify .

Apply the distributive property.

Multiply by .

Move all terms containing to the left side of the equation.

Add to both sides of the equation.

Add and .

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

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

List all of the solutions.

Verify each of the solutions by substituting them into and solving.

Solve for z |z+9|=|z-9|