Solution: Compute $ h(3) = 9 - 12 + m = -3 + m $ and $ k(1) = 1 - 4 + 2m = -3 + 2m $. Set equal: $ -3 + m = -3 + 2m $. Simplify: $ 0 = m $, so $ m = \boxed{0} $.

["Mastering Linear Equations: Solving for $ m $ Using Simple Substitution", "In algebra, solving for unknowns like $ m $ is a foundational skill that appears frequently in equations, word problems, and real-world applications. This article explores a clear and step-by-step method for solving a linear equation involving an unknown variable $ m $, using substitution and simplification techniques—perfect for students and learners aiming to strengthen their problem-solving skills.", "We begin with two expressions representing values dependent on $ m $:\n$$\nh(3) = 9 - 12 + m = -3 + m\n$$\n$$\nk(1) = 1 - 4 + 2m = -3 + 2m\n$$", "The problem sets these equal to model a relationship:\n$$\nh(3) = k(1)\n\Rightarrow -3 + m = -3 + 2m\n$$", "### Step-by-Step Solution", "1. Set the expressions equal:\nStart with the equation derived from substitution:\n$$\n-3 + m = -3 + 2m\n$$", "2. Subtract $ -3 $ from both sides:\n$$\nm = 2m\n$$", "3. Subtract $ m $ from both sides:\n$$\n0 = m\n$$", "Hence, the solution is:\n$$\nm = \boxed{0}\n$$", "### Why This Method Works", "This approach uses substitution and simplification—key techniques for solving linear equations. By eliminating constants through intelligent rearrangement, we isolate the variable cleanly. This method builds logical thinking and is essential for tackling more complex equations involving multiple variables and operations.", "### Real-World Application", "Such equations model scenarios where two expressions represent competing forces, costs, or rates—like comparing profits, measuring material needed, or balancing budgets. Knowing how to solve for unknowns enables better decision-making and problem-solving across disciplines.", "---", "Mastering these basic steps unlocks greater confidence in algebra and sets the stage for advanced mathematical reasoning. Whether through textbooks, tutoring, or practice problems, consistently working through substitutions and simplifications pays long-term dividends in academic and real-life contexts."]