Factor: \( (x - 12)(x + 10) = 0 \) → \( x = 12 \) (since \( x > 0 \))

["### Solving the Factor Equation: ( (x - 12)(x + 10) = 0 ) \nStep-by-Step Guide to Find ( x = 12 ) (with ( x > 0 ))", "When faced with an equation like ( (x - 12)(x + 10) = 0 ), solving it becomes straightforward using basic algebraic principles. This article explains how to solve the equation and why the only valid solution is ( x = 12 ), given the condition ( x > 0 ).", "---", "#### Understanding the Zero Product Property\nThe equation ( (x - 12)(x + 10) = 0 ) relies on a fundamental rule in algebra: the zero product property. This property states:", "> If the product of two factors is zero, then at least one of the factors must be zero.", "In mathematical terms:\nIf ( A \cdot B = 0 ), then ( A = 0 ) or ( B = 0 ) (or both).", "Applying this to our equation:\nEither ( x - 12 = 0 ) or ( x + 10 = 0 ).", "---", "#### Step 1: Solve Each Factor Equal to Zero", "- Solve ( x - 12 = 0 ):\n Add 12 to both sides →\n ( x = 12 )", "- Solve ( x + 10 = 0 ):\n Subtract 10 from both sides →\n ( x = -10 )", "---", "#### Step 2: Apply the Constraint ( x > 0 )", "From the two solutions ( x = 12 ) and ( x = -10 ), we must choose the one that satisfies ( x > 0 ).", "- ( x = 12 ) → positive ✅\n- ( x = -10 ) → negative ❌", "Thus, the only valid solution is:", "[\nx = 12\n]", "---", "#### Why This Matters: Real-World Applications", "Solving such equations is foundational in many scientific and engineering fields. For instance:\n- Physics: Finding time points where displacement equals zero.\n- Economics: Determining break-even points in profit models.\n- Engineering: Stabilizing systems by locating equilibrium conditions.", "Answering equations precisely ensures accurate modeling and reliable outcomes.", "---", "#### Summary", "To solve ( (x - 12)(x + 10) = 0 ):\n1. Set each factor to zero.\n2. Solve for ( x ): ( x = 12 ) and ( x = -10 ).\n3. Apply constraints—only ( x = 12 ) satisfies ( x > 0 ).", "This client-side algebraic method efficiently narrows results and ensures correctness.", "---", "#### Key Takeaway", "> When solving multiplicative equations set to zero, remember the zero product property and carefully apply given constraints to yield practical, valid solutions.", "---", "### Key Terms for SEO:\nFactor equation, solve (x - 12)(x + 10) = 0, x = 12, algebraic solution, zero product property, positive solutions, quadratic factors, equation basics, step-by-step algebra.", "---", "Optimize your understanding:\nUse this method whenever you encounter root-zero equations—especially in math homework, technical exams, or real-world problem-solving scenarios requiring precise, logical outcomes."]