Not all equations are equated to zero, but usually we set a function equal to zero if we want to find its x intercepts, or where the graph of the function crosses the x axis.
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I am not entirely sure what kind of equation you want to solve. Anyway, if an expression has an exponent of zero, the entire expression is usually equal to 1 (unless you raise zero to the power zero; that's undefined). Perhaps that can help you simplify the expression. For example: if you have an equation such as (x+y+z)0 + 5x + 3 = 10 The entire left expression, (x+y+z)0 can be replaced with 1, thus simplifying the equation.
A horizontal line has a slope of zero. The equation of a horizontal line is y = a.
That its roots (solutions) are coincident.
Technically is can be anything you want it to be since you did not equate this expression to any value.
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.