-3t^2 + 12 = 0 \Rightarrow t^2 = 4 \Rightarrow t = 2 \quad (\text{since } t \geq 0).

["# Solving the Quadratic Equation: -3t² + 12 = 0 — Finding t with t ≥ 0", "Solving quadratic equations is a fundamental skill in algebra, and understanding how to isolate and solve for variables properly is key to succeeding in math studies. One common problem students encounter is equations like -3t² + 12 = 0. In this article, we dive into clearly explaining how to solve this equation step-by-step and arrive at the solution t = 2, with the condition that t ≥ 0.", "---", "## Step-by-Step Solution to –3t² + 12 = 0", "### Step 1: Start with the original equation\nThe equation to solve is:\n[\n-3t^2 + 12 = 0\n]", "### Step 2: Isolate the quadratic term\nSubtract 12 from both sides:\n[\n-3t^2 = -12\n]", "### Step 3: Divide both sides by –3\nDividing both sides by –3 flips the sign and simplifies the coefficient:\n[\nt^2 = \frac{-12}{-3} = 4\n]", "This gives:\n[\nt^2 = 4\n]", "---", "## Step 4: Take the square root of both sides", "To solve for t, take the square root of both sides:\n[\nt = \pm\sqrt{4} = \pm 2\n]", "This means t = 2 or t = –2. However, since the problem specifies t ≥ 0, we discard the negative solution.", "### Final Step: Express the valid solution\n[\nt = 2\n]", "---", "## Why t ≥ 0 Matters", "In real-world applications, variables like time, distance, or negative square roots rarely make sense unless context supports them. Specifying t ≥ 0 ensures we focus only on physically meaningful solutions.", "---", "## Summary", "- Starting from: –3t² + 12 = 0\n- After isolating t²: t² = 4\n- Taking square roots: t = ±2\n- Restricting to t ≥ 0: t = 2", "This simple quadratic equation reveals how algebraic manipulation and domain restrictions guide us to the correct, applicable solution.", "---", "## Key Takeaways\n- Always isolate the quadratic term first.\n- Use inverse operations carefully to isolate variables.\n- Check the context and constraints—here, t ≥ 0 narrowed the solution.\n- Practicing such steps builds mastery of quadratic equations essential for advanced math and science applications.", "---", "By understanding each step and the reasoning behind solving for t, you empower yourself to tackle similar equations confidently and correctly."]