var test = {
  'op': 'equal',

    'lhs': {
        'op': 'add',
        'lhs': 1,
        'rhs': {
            'op': 'multiply',
            'lhs': 'x',
            'rhs': 10
        }
    },

    'rhs': 21
};


function strToOp(str){
  switch(str){
    case 'add':
      return '+';
    case 'multiply':
      return '*';
    case 'divide':
      return '/';
    case 'subtract':
      return '-';
    case 'equal':
      return '=';
  }
}

var my_string = "";

function makeString(myObj){
    if(typeof myObj === 'object'){
        my_string+= '(';
        makeString(myObj['lhs']);
        my_string+= strToOp(myObj.op);
        if(typeof myObj['rhs'] === 'object'){
            makeString(myObj['rhs']);
            my_string+= ')';
        }else{
            makeString(myObj['rhs']);
            my_string+= ')';
        }
    }else{
        my_string+= myObj;
    }
}

function opposite_op(str){
    switch(str){
    case 'add':
      return 'subtract';
    case 'multiply':
      return 'divide';
    case 'divide':
      return 'multiply';
    case 'subtract':
      return 'add';
    case 'rhs':
        return 'lhs';
    case 'lhs':
        return 'rhs';
  }
}


function srch(obj){
    //search for x in obj; if Found return true else false

    if(typeof obj === 'object'){
        return srch(obj['lhs']) || srch(obj['rhs']);

    }

    if(obj==='x'){
        return true;
    }else{
        return false;
    }
}

function has_x(obj){
    //obj['lhs'] is passed in this function;
    //will return 'lhs' or 'rhs'

    if(srch(obj['lhs'])){
        return 'lhs';
    }else{
        return 'rhs';
    }
}

function transfer_lhs_rhs(obj){
    obj['rhs'] = {'lhs': obj['rhs']};
    obj['rhs']['op'] = opposite_op(obj['lhs']['op']);
    obj['rhs']['rhs'] = obj['lhs'][opposite_op(has_x(obj['lhs']))];


    obj['lhs'] = obj['lhs'][has_x(obj['lhs'])];

    if(obj['lhs'] !== 'x'){
        transfer_lhs_rhs(obj);
    }
}

makeString(test);
var result1 = my_string.slice(1, -1);
console.log(result1);

my_string = "";
transfer_lhs_rhs(test);
makeString(test);
var result2 = my_string.slice(1, -1);
console.log(result2);

var to_eval = result2.substring(result2.indexOf('=')+1, result2.length);
//console.log(to_eval);

console.log("x = " + eval(to_eval));