Cela se simplifie en \( 110 = \frac{n}{2}(10 + 3n - 3) \) ou \( 110 = \frac{n}{2}(3n + 7) \).

["Title: Simplifying a Quadratic Equation: How to Solve ( 110 = \frac{n}{2}(10 + 3n - 3) )", "Meta Description:\nLearn how to simplify the equation ( 110 = \frac{n}{2}(10 + 3n - 3) ) into the standard quadratic form ( 110 = \frac{n}{2}(3n + 7) ), step-by-step. Ideal for students and math enthusiasts.", "---", "## How to Simplify the Equation ( 110 = \frac{n}{2}(10 + 3n - 3) )", "Solving linear equations is straightforward, but sometimes expressions appear complex before being simplified into a familiar quadratic form. One such case is simplifying the equation:", "[\n110 = \frac{n}{2}(10 + 3n - 3)\n]", "In this article, we’ll break down how to simplify this expression step-by-step, ending up with the standard quadratic form ( 110 = \frac{n}{2}(3n + 7) ).", "---", "### Step 1: Simplify the Expression Inside the Parentheses", "Start with the original equation:", "[\n110 = \frac{n}{2}(10 + 3n - 3)\n]", "First, combine like terms inside the parentheses:", "[\n10 + 3n - 3 = 3n + 7\n]", "Now substitute back:", "[\n110 = \frac{n}{2}(3n + 7)\n]", "This matches the simplified form you wanted:\n[\n110 = \frac{n}{2}(3n + 7)\n]", "---", "### Step 2: Eliminate the Fraction by Multiplying Both Sides", "To simplify further and convert to a quadratic equation, multiply both sides of the equation by 2:", "[\n2 \ imes 110 = n(3n + 7)\n]", "[\n220 = n(3n + 7)\n]", "---", "### Step 3: Distribute and Rearrange Into Standard Quadratic Form", "Expand the right-hand side:", "[\n220 = 3n^2 + 7n\n]", "Bring all terms to one side to form a standard quadratic equation:", "[\n3n^2 + 7n - 220 = 0\n]", "---", "### Final Equation", "Thus, the simplified quadratic form is:", "[\n\boxed{110 = \frac{n}{2}(3n + 7)} \quad \ ext{leads to} \quad 3n^2 + 7n - 220 = 0\n]", "This quadratic equation can now be solved using standard methods such as factoring, completing the square, or the quadratic formula.", "---", "### Why This Matters", "Understanding how complex expressions reduce to simpler quadratic forms is essential for algebra, calculus, and real-world problem solving. Simplifying equations like:", "[\n110 = \frac{n}{2}(10 + 3n - 3)\n]", "into ( 110 = \frac{n}{2}(3n + 7) ) enables efficient step-by-step solution strategies.", "---", "### Summary", "1. Combine constants inside the parentheses: ( 10 + 3n - 3 = 3n + 7 )\n2. Replace in the equation: ( 110 = \frac{n}{2}(3n + 7) )\n3. Multiply both sides by 2 to eliminate the fraction\n4. Expand and rearrange into standard quadratic form", "With practice, simplifying equations becomes intuitive—key to mastering algebra and beyond.", "---", "Keywords: quadratic equation simplification, solving (110 = \frac{n}{2}(10 + 3n - 3)), simplify (110 = \frac{n}{2}(3n + 7)), algebra steps, solving quadratics, equation simplification technique, math problem solving.", "---", "If you found this guide helpful, share it with fellow students or dive deeper into quadratic equations and their applications!"]