Question

solve the following quadratic equation using the zero product property.
6(4 - x)(x + 3) = 0
the solution set is
(type an integer or a simplified fraction. use a comma to separate answers as needed. type ea

Explanation:

Step1: Analyze the zero product property

The zero product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). In the equation \(6(4 - x)(x + 3)=0\), we have three factors: \(6\), \((4 - x)\), and \((x + 3)\). Since \(6
eq0\) (a non - zero constant), we set the other two factors equal to zero.

Step2: Solve for \(x\) when \(4 - x=0\)

We solve the equation \(4 - x = 0\) for \(x\).
Subtract \(4\) from both sides: \(-x=- 4\).
Multiply both sides by \(- 1\): \(x = 4\).

Step3: Solve for \(x\) when \(x + 3=0\)

We solve the equation \(x+3 = 0\) for \(x\).
Subtract \(3\) from both sides: \(x=-3\).

Answer:

\(4, - 3\)