Make a detailed explanation for this quadratic equation---**Mathematical Formula:** x² + 4x + 3 = 0

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Let's explore the quadratic equation x squared plus 4x plus 3 equals zero. A quadratic equation is a polynomial equation of degree 2, written in the standard form ax squared plus bx plus c equals zero, where a is not equal to zero. In our specific equation, we can identify the coefficients: a equals 1, b equals 4, and c equals 3. This parabola opens upward and crosses the x-axis at two points, which represent the solutions to our equation. Now let's solve this equation using the factoring method. To factor x squared plus 4x plus 3, we need to find two numbers that multiply to give 3 and add to give 4. Looking at the factor pairs of 3, we have 1 times 3 equals 3, and 1 plus 3 equals 4, which works perfectly. So we can write x squared plus 4x plus 3 as the product of x plus 1 and x plus 3. Setting each factor equal to zero gives us x equals negative 1 and x equals negative 3. We can verify this by expanding the factored form back to the original equation.