(3+5x)(2-3x)=12-15x^2

2 min read Jun 16, 2024
(3+5x)(2-3x)=12-15x^2

Solving the Equation: (3 + 5x)(2 - 3x) = 12 - 15x^2

This equation presents a challenge that requires us to manipulate algebraic expressions to find a solution. Let's break down the steps:

1. Expanding the Left Side

The left side of the equation involves multiplying two binomials. We can use the distributive property (or the FOIL method) to expand it:

(3 + 5x)(2 - 3x) = (3 * 2) + (3 * -3x) + (5x * 2) + (5x * -3x)

Simplifying this gives us:

6 - 9x + 10x - 15x²

2. Rewriting the Equation

Now, our equation looks like this:

6 - 9x + 10x - 15x² = 12 - 15x²

3. Simplifying the Equation

Notice that the -15x² terms cancel out on both sides:

6 - 9x + 10x = 12

Combining like terms on the left side:

6 + x = 12

4. Isolate the Variable (x)

To solve for 'x', we need to isolate it. Subtracting 6 from both sides:

x = 12 - 6

5. The Solution

Finally, we have our answer:

x = 6

Therefore, the solution to the equation (3 + 5x)(2 - 3x) = 12 - 15x² is x = 6.

Related Post