Purpose – Mathematical problem solving in Basic Mathematics requires first-year university students to interpret information, select relevant concepts, apply algebraic procedures, and justify conclusions coherently. However, students’ incorrect or incomplete responses cannot be adequately interpreted through right-or-wrong scoring alone. This study aims to analyse first-year students’ errors in transforming equations into the standard form of quadratic equations using the Structure of Observed Learning Outcomes (SOLO) Taxonomy. Methodology – This study employed a descriptive qualitative approach. The data were obtained from a representative written response produced by a first-year university student enrolled in a Basic Mathematics course. The student’s solution was analysed by identifying the location of errors, classifying the types of errors, and mapping the structural quality of the response into SOLO levels: prestructural, unistructural, multistructural, relational, and extended abstract. Findings – The findings show that the student demonstrated meaningful but inconsistent algebraic understanding. The student correctly transformed some equations into standard quadratic form and identified the coefficients (a), (b), and (c). However, errors occurred in expansion, sign manipulation, simplification, and algebraic justification. The overall response was classified as multistructural with emerging relational characteristics, indicating that the student used several relevant procedures but did not consistently integrate them into a coherent and accurate solution. Novelty – This study contributes an integrated analytical framework that combines error analysis and the SOLO Taxonomy to interpret both the types of mathematical errors and the structural quality of students’ responses. Significance – The findings may assist Basic Mathematics lecturers in designing diagnostic feedback, assessment rubrics, and instructional interventions that support students’ transition from procedural performance to relational understanding.