Questions: (6x+7)(5x-8)=0 x= (Simplify your answer. Type each solution only once. Use a comma to separate answers as needed)

Solution Steps

To solve the equation \((6x + 7)(5x - 8) = 0\), we can use the zero-product property. This property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for \(x\).

1. Set \(6x + 7 = 0\) and solve for \(x\).
2. Set \(5x - 8 = 0\) and solve for \(x\).
3. The solutions to these equations will be the solutions to the original equation.

Given the equation \((6x + 7)(5x - 8) = 0\), we apply the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero:

1. \(6x + 7 = 0\)
2. \(5x - 8 = 0\)

Solve each equation for \(x\):

1. For \(6x + 7 = 0\): \[ 6x + 7 = 0 \implies 6x = -7 \implies x = -\frac{7}{6} \]

2. For \(5x - 8 = 0\): \[ 5x - 8 = 0 \implies 5x = 8 \implies x = \frac{8}{5} \]

Final Answer