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. Start by identifying the quadratic equation: \(4x^2 + 16x + 12 = 0\).
2. Check if the quadratic can be simplified by factoring. Look for two numbers that multiply to \(4 \times 12 = 48\) and add to \(16\).
3. The numbers 12 and 4 satisfy these conditions, so rewrite the middle term: \(4x^2 + 12x + 4x + 12 = 0\).
4. Group the terms: \((4x^2 + 12x) + (4x + 12) = 0\) and factor by grouping: \(4x(x + 3) + 4(x + 3) = 0\).
5. Factor out the common factor \((x + 3)\): \((4x + 4)(x + 3) = 0\). Set each factor to zero and solve for \(x\): \(4x + 4 = 0\) and \(x + 3 = 0\).