Factor the quadratic: \( 3(x^2 - 4x + 3) = 0 \).

["SEO-Optimized Article: How to Factor the Quadratic Equation ( 3(x^2 - 4x + 3) = 0 )", "---", "### Master Factoring Quadratic Equations: Solve ( 3(x^2 - 4x + 3) = 0 ) with Step-by-Step Guide", "Factoring quadratics is a fundamental skill in algebra that helps students simplify equations, find roots, and solve real-world problems. One common challenge is factoring expressions like ( 3(x^2 - 4x + 3) = 0 ), especially when a coefficient other than 1 multiplies the quadratic. In this article, you’ll learn exactly how to factor this quadratic expression and solve the equation efficiently.", "---", "### Understanding the Equation", "Start with the equation:\n[\n3(x^2 - 4x + 3) = 0\n]", "Software and calculators can solve it quickly, but knowing how to factor manually builds strong algebra skills. Factoring relies on expressing a quadratic in the form ( a(x - p)(x - q) = 0 ), where ( p ) and ( q ) are the roots. However, when a non-1 coefficient multiplies the quadratic, you must factor by grouping or use strategic decomposition.", "---", "### Step-by-Step Factorization of ( x^2 - 4x + 3 )", "First, focus on factoring the inner quadratic expression:\n[\nx^2 - 4x + 3\n]", "We look for two numbers that:\n- Multiply to ( +3 ) (the constant term)\n- Add up to ( -4 ) (the linear coefficient)", "The pair ( -1 ) and ( -3 ) satisfies this:\n[\n-1 \ imes -3 = 3 \quad \ ext{and} \quad -1 + (-3) = -4\n]", "So, the quadratic factors as:\n[\nx^2 - 4x + 3 = (x - 1)(x - 3)\n]", "Now include the leading coefficient of 3 in the original expression:\n[\n3(x^2 - 4x + 3) = 3(x - 1)(x - 3)\n]", "---", "### Solving the Factored Equation", "Putting it all together:\n[\n3(x - 1)(x - 3) = 0\n]", "Using the Zero Product Property, set each factor equal to zero:\n[\nx - 1 = 0 \quad \Rightarrow \quad x = 1\n]\n[\nx - 3 = 0 \quad \Rightarrow \quad x = 3\n]", "---", "### Final Solution", "The solutions to the equation ( 3(x^2 - 4x + 3) = 0 ) are:\n[\n\boxed{x = 1 \quad \ ext{and} \quad x = 3}\n]", "---", "### Why Factoring Matters", "Factoring quadratics with leading coefficients allows you to:\n- Find zeros of quadratic functions smoothly\n- Graph parabolas accurately by identifying roots and vertex\n- Solve equations that model real-life scenarios, like projectile motion or economics", "Memorizing factoring patterns and practicing strategically ensures you’re ready for more advanced math topics like quadratic equations, systems of equations, and beyond.", "---", "### Keywords for SEO Optimization:\nQuadratic factoring, factor trinomial, solve quadratic equations, factor ( x^2 - 4x + 3 ), factor with leading coefficient, zero product property, algebra practice, quadratic roots.", "---", "Grab your notebook and start factoring—remember, every quadratic has its story waiting to be uncovered!", "---", "If you found this guide helpful, share it with fellow students or check out more algebra tutorials on factoring complex quadratics.", "---", "Meta Title: Factor ( 3(x^2 - 4x + 3) = 0 ) – Step-by-Step Factoring Guide\nMeta Description: Learn how to factor ( 3(x^2 - 4x + 3) = 0 ) using grouping and zero product rule. Find solutions and master quadratic solving techniques.\nTags: #FactoringQuadratics #AlgebraTutorial #SolveQuadratic #QuadraticEquations #MathHelp #AcademicResources"]