Algebraic expressions can't be solved because they are not equations but they can be simplified.
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A quadratic equation can be solved by completing the square which gives more information about the properties of the parabola than with the quadratic equation formula.
If you mean 3x2+4x-2 = 0 then it can be solved by means of the quadratic equation formulla
No, you can only simplify an expression. To solve for a variable, it must be in an equation.
No, but they are symmetric with respect to a line parallel to the y-axis - which could be the y-axis itself.
z + 8 - 2 is an expression, not an equation. An expression cannot be solved. At best, you can simplify it to z + 6.