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 ('+-*/^()='.includes(expr[i])) { tokens.push({ type: 'OPERATOR', value: expr[i++] }); continue;