How to Solve the Equation (3x-2)(x+4)=24

TL;DR

To solve the equation (3x-2)(x+4)=24, first expand it to get 3x² + 10x - 32 = 0. Then, factor it to (3x + 16)(x - 2) = 0 and apply the zero product property. The solutions are x = -16/3 and x = 2.

Transcript

we are going to solve this equation we have 3x - 2 * x + 4 and this is equal to 24 let me show you what's wrong first don't get too excited because we see we have two factors on the left hand side but then don't just say I'm going to set this is equal to that and then say 3x - 2 is equal to 24 and then x + 4 is equal to 24 and then you continue fro... Read More

Key Insights

• 😫 Setting factors equal to a number other than zero is incorrect in equation solving.
• 🍳 By factoring equations, we can break them down and solve for different variables.
• 🧑‍🏭 The take-ttle method is useful in factoring three-term polynomials.

Questions & Answers

Q: Why can't we directly set the factors equal to 24?

We can only set factors equal to zero. Setting them equal to 24 would not produce the correct result.

Q: How do we solve equations that have factors other than zero?

In such cases, we need to multiply out the equation first, then subtract the desired value from both sides to create a zero on one side.

Q: What is the purpose of factoring an equation?

Factoring allows us to break down complex equations into simpler forms, making it easier to find the solutions.

Q: What is the zero product property?

The zero product property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Summary & Key Takeaways

• Factoring out the equation 3x - 2 * x + 4 = 24 gives 3x² + 10x - 32 = 0.

• Using the take-ttle method, the equation factors to (3x + 16)(x - 2) = 0.

• Solving for x yields x = -16/3 and x = 2 as the correct answers.