Simplify: \( 2(3w + 3) = 54 \) → \( 6w + 6 = 54 \).

["# Simplify: ( 2(3w + 3) = 54 ) — Step-by-Step Algebraic Solution", "If you're trying to solve ( 2(3w + 3) = 54 ), simplifying this equation step-by-step makes finding the value of ( w ) much easier. Whether you're learning algebra for the first time or brushing up on basic equations, mastering how to simplify and solve linear expressions is essential. In this article, we’ll walk through the process of simplifying ( 2(3w + 3) = 54 ), solving for ( w ), and understanding the logic behind each step.", "### Starting Equation\nBegin with the original equation:\n[\n2(3w + 3) = 54\n]\nThis expression shows that two times the quantity ( (3w + 3) ) equals 54. Our goal is to isolate ( w ).", "### Step 1: Distribute the 2\nFirst, simplify the left-hand side by eliminating the parentheses using the distributive property of multiplication over addition:\n[\n2 \cdot 3w + 2 \cdot 3 = 54\n]\n[\n6w + 6 = 54\n]\nNow the equation becomes simpler: ( 6w + 6 = 54 ).", "### Step 2: Subtract 6 from Both Sides\nTo isolate the term with ( w ), subtract 6 from both sides:\n[\n6w + 6 - 6 = 54 - 6\n]\n[\n6w = 48\n]\nThis eliminates the constant, leaving only the term with ( w ) on the left.", "### Step 3: Divide by 6\nNow solve for ( w ) by dividing both sides by 6:\n[\n\frac{6w}{6} = \frac{48}{6}\n]\n[\nw = 8\n]", "### Final Answer\n[\n\boxed{w = 8}\n]", "### Why This Works: A Quick Recap\n- Distributive Property allows us to multiply ( 2 ) across ( (3w + 3) ).\n- Simplifying both sides reduces complexity and makes isolating ( w ) straightforward.\n- Basic algebra steps—subtracting, then dividing—keep the equation balanced and ensure the solution is correct.", "Understanding how to simplify expressions like ( 2(3w + 3) = 54 ) builds foundational skills for solving more complex equations. Keep practicing, and you’ll master these methods in no time!", "If you want more math help, explore other linear equations, factoring, or algebraic expressions—hard skills that pay off every day.", "---\nKeywords: algebraic equation solving, simplify 2(3w + 3) = 54, solve for w, step-by-step algebra, linear equation, elementary math tutorial."]