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

(6x+7)(5x-8)=0 x= (Simplify your answer. Type each solution only once. Use a comma to separate answers as needed)
Transcript text: \[ \begin{array}{l} (6 x+7)(5 x-8)=0 \\ x=\square \end{array} \] (Simplify your answer. Type each solution only once Use a comma to separate answers as needed)
failed

Solution

failed
failed

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.
Step 1: Apply the Zero-Product Property

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. \(5x - 8 = 0\)
Step 2: Solve Each Equation

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

\(\boxed{x = -\frac{7}{6}, \frac{8}{5}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Setting up child-care centers, encouraging an employee to wear his hearing aid, and providing great insurance and benefits are all ways to: Increase awareness of diversity Allow employees to network Provide diversity skills Accommodate special needs As a result of the policies at Mitchell Gold + Bob Williams, female employees are more likely to: Opt out of work Be stopped by glass walls Encounter a glass ceiling
failedAnswered
Question 2 1 pts In response to Glaucon's claim about why one acts morally (Ring of Gyges), Socrates claims what? Select the BEST possible answer. The gods will punish those who are immoral. Those who are not philosophers lack true moral agency. Immoral acts poison the soul. It is not in one's nature to act immorally. Next 1 Previous
failedAnswered
A channel, also known as the is the method a sender uses to deliver a message.
failedAnswered
Chapter 15: "What Is Freedom?": Reconstruction, 1865-1877 15.3. What were the social and political effects of Radical Reconstruction in the South? Match the descriptions of white Republicans in the South during Reconstruction to the correct term. These northern whites relocated to the South after the Civil War. Southern whites believed they had come simply for economic gain. These southern whites supported the Republicans and had not supported secession or the Confederacy. These were wartime Unionists from the South who hoped Reconstruction governments would help them recover from wartime economic losses. Some were investors in land and railroads who saw the postwar South as an opportunity to combine personal financial gain with a role in helping to substitute "the civilization of freedom for that of slavery."
failedAnswered
Quiz Solve the following equation for x. e^(x^2-4x)=e^12 x= (Type an integer or a decimal. Use a comma to