Parsing Math Equations in JavaScript: From String to Solution

Building a math equation solver that accepts text input like "2x + 5 = 13" and returns "x = 4" is one of those projects that sounds straightforward and then quickly reveals the depth of parsing, algebra, and numerical methods. Here is how it works. Step 1: Tokenization The first step is breaking the input string into meaningful tokens. For "2x + 5 = 13", the tokens are: [NUMBER:2, VARIABLE:x, OPERATOR:+, NUMBER:5, EQUALS:=, NUMBER:13] function tokenize ( expr ) { const tokens = []; let i = 0 ; while ( i < expr . length ) { if ( / \s / . test ( expr [ i ])) { i ++ ; continue ; } if ( / \d / . test ( expr [ i ]) || ( expr [ i ] === ' . ' && / \d / . test ( expr [ i + 1 ]))) { let num = '' ; while ( i < expr . length && / [\d . ] / . test ( expr [ i ])) num += expr [ i ++ ]; tokens . push ({ type : ' NUMBER ' , value : parseFloat ( num ) }); continue ; } if ( / [ a-z ] /i . test ( expr [ i ])) { tokens . push ({ type : ' VARIABLE ' , value : expr [ i ++ ] }); continue ; } if ( ' +-*/^()=