(2-3x)%3D12-15x%5E2.jpeg "(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.