Choose and apply the best method to solve the given quadratic equation. 
$4x^2+16x+12=0$

• A. $x=-3,x=-1$
• B. $x=3,x=1$
• C. $x=3,x=4$
• D. $x=-12,x=1$

Answer: (A)

Verified step by step guidance

1. First, identify the quadratic equation given: \(4x^2 + 16x + 12 = 0\).
2. To simplify the equation, divide all terms by 4, the greatest common factor, resulting in \(x^2 + 4x + 3 = 0\).
3. Next, factor the quadratic equation. Look for two numbers that multiply to 3 (the constant term) and add to 4 (the coefficient of the linear term).
4. The numbers 1 and 3 satisfy these conditions, so the equation can be factored as \((x + 1)(x + 3) = 0\).
5. Apply the zero product property: set each factor equal to zero, \(x + 1 = 0\) and \(x + 3 = 0\), and solve for \(x\) to find the solutions.