Solving the Equation: (x+1)(4x2) = (2x1)(3x1)
This article will guide you through solving the equation (x+1)(4x2) = (2x1)(3x1).
Expanding Both Sides
The first step is to expand both sides of the equation using the distributive property (also known as FOIL).
 Left Side: (x+1)(4x2) = 4x²  2x + 4x  2 = 4x² + 2x  2
 Right Side: (2x1)(3x1) = 6x²  2x  3x + 1 = 6x²  5x + 1
Now, our equation looks like this: 4x² + 2x  2 = 6x²  5x + 1
Simplifying the Equation
To make the equation easier to solve, we'll move all the terms to one side:
 Subtract 4x² from both sides: 2x  2 = 2x²  5x + 1
 Add 5x to both sides: 7x  2 = 2x² + 1
 Subtract 1 from both sides: 7x  3 = 2x²
Now we have a quadratic equation: 2x²  7x + 3 = 0
Solving the Quadratic Equation
We can solve this quadratic equation using the quadratic formula:
x = (b ± √(b²  4ac)) / 2a
Where:
 a = 2
 b = 7
 c = 3
Plugging these values into the quadratic formula:
x = (7 ± √((7)²  4 * 2 * 3)) / (2 * 2)
x = (7 ± √(49  24)) / 4
x = (7 ± √25) / 4
x = (7 ± 5) / 4
This gives us two possible solutions:
 x = (7 + 5) / 4 = 3
 x = (7  5) / 4 = 1/2
Checking the Solutions
It's always a good idea to check our solutions by plugging them back into the original equation.

For x = 3:
 (3+1)(432) = (231)(3*31)
 4 * 10 = 5 * 8
 40 = 40 (This solution works)

For x = 1/2:
 (1/2+1)(4*(1/2)2) = (2*(1/2)1)(3*(1/2)1)
 (3/2) * 0 = 0 * (1/2)
 0 = 0 (This solution also works)
Conclusion
Therefore, the solutions to the equation (x+1)(4x2) = (2x1)(3x1) are x = 3 and x = 1/2.