Solve for z |z+10|=|z-8|

Math
Rewrite the absolute value equation as four equations without absolute value bars.
After simplifying, there are only two unique equations to be solved.
Solve for .
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Move all terms containing to the left side of the equation.
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Subtract from both sides of the equation.
Combine the opposite terms in .
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Subtract from .
Add and .
Since , there are no solutions.
No solution
No solution
Solve for .
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Simplify .
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Apply the distributive property.
Multiply by .
Move all terms containing to the left side of the equation.
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Add to both sides of the equation.
Add and .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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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+10|=|z-8|

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