diff --git a/lib/solveEquation/stepThrough.js b/lib/solveEquation/stepThrough.js
index 64380c72..e3ca243c 100644
--- a/lib/solveEquation/stepThrough.js
+++ b/lib/solveEquation/stepThrough.js
@@ -42,8 +42,7 @@ function stepThrough(leftNode, rightNode, comparator, debug=false) {
   if (symbolSet.size === 0) {
     return solveConstantEquation(equation, debug);
   }
-  const symbolName = symbolSet.values().next().value;
-
+  let symbolName = symbolSet.values().next().value;
   let equationStatus;
   let steps = [];
 
@@ -80,8 +79,13 @@ function stepThrough(leftNode, rightNode, comparator, debug=false) {
     equation.rightNode = flattenOperands(equation.rightNode);
 
     // at this point, the symbols might have cancelled out.
-    if (Symbols.getSymbolsInEquation(equation).size === 0) {
+    const postSimplificationSymbols = Symbols.getSymbolsInEquation(equation)
+    if (postSimplificationSymbols.size === 0) {
+      // if all symbols are canceled out, the equation can now be treated as a constant equation
       return solveConstantEquation(equation, debug, steps);
+    } else if (!postSimplificationSymbols.has(symbolName)) {
+      // if the original symbol is canceled out but other sybols remain, reset the target symbol
+      symbolName = postSimplificationSymbols.values().next().value;
     }
 
     // The left side of the equation is either factored or simplified.
diff --git a/test/solveEquation/solveEquation.test.js b/test/solveEquation/solveEquation.test.js
index c92d304a..ef85d748 100644
--- a/test/solveEquation/solveEquation.test.js
+++ b/test/solveEquation/solveEquation.test.js
@@ -96,7 +96,9 @@ describe('solveEquation for =', function () {
     ['(3 + x) / (x^2 + 3) = 1', 'x = [0, 1]'],
     ['6/x + 8/(2x) = 10', 'x = 1'],
     ['(x+1)=4', 'x = 3'],
-    ['((x)/(4))=4', 'x = 16']
+    ['((x)/(4))=4', 'x = 16'],
+    ['x+y=x+y', '0 = 0'],
+    ['y + 2x = 14 + y', 'x = 7']
     // TODO: fix these cases, fail because lack of factoring support, for complex #s,
     // for taking the sqrt of both sides, etc
     // ['(x + y) (y + 2) = 0', 'y = -y'],
@@ -155,6 +157,7 @@ describe('constant comparison support', function () {
     ['1 <= 1', ChangeTypes.STATEMENT_IS_TRUE],
     ['2 <= 1', ChangeTypes.STATEMENT_IS_FALSE],
     ['1 <= 2', ChangeTypes.STATEMENT_IS_TRUE],
+    ['0 = 0', ChangeTypes.STATEMENT_IS_TRUE],
     ['( 1) = ( 14)', ChangeTypes.STATEMENT_IS_FALSE],
     // TODO: when we support fancy exponent and sqrt things
     // ['(1/64)^(-5/6) = 32', ChangeTypes.STATEMENT_IS_TRUE],