Solve the quadratic equation by factoring out the GCF: 12x2+20x=0

Question

(3 points)
GCF:

List smaller solution first: x=

and x=

Answer 1

To solve the quadratic equation \(12x^2 + 20x = 0\), we start by factoring out the greatest common factor (GCF) from the expression.

1. Identify the GCF of the coefficients \(12\) and \(20\). The GCF is \(4\). So, we factor out \(4x\):

\[ 12x^2 + 20x = 4x(3x + 5) = 0 \]

2. Set each factor equal to zero:

\[ 4x = 0 \quad \text{and} \quad 3x + 5 = 0 \]

3. Solve the first equation:

\[ 4x = 0 \implies x = 0 \]

4. Solve the second equation:

\[ 3x + 5 = 0 \implies 3x = -5 \implies x = -\frac{5}{3} \]

Now we can write the solutions. The smaller solution should be listed first:

• Smaller solution: \(x = -\frac{5}{3}\)
• Larger solution: \(x = 0\)

In summary:

GCF: \(4x\)

List smaller solution first:

• \(x = -\frac{5}{3}\)
• \(x = 0\)