Solving the Equation (x+1)(x7) = (x1)(x+3)
This article will guide you through the steps to solve the equation (x+1)(x7) = (x1)(x+3).
Expanding the Equation
The first step is to expand both sides of the equation by using the distributive property (also known as FOIL  First, Outer, Inner, Last):
 Left Side: (x+1)(x7) = x(x7) + 1(x7) = x²  7x + x  7 = x²  6x  7
 Right Side: (x1)(x+3) = x(x+3)  1(x+3) = x² + 3x  x  3 = x² + 2x  3
Now our equation looks like this: x²  6x  7 = x² + 2x  3
Simplifying and Solving
Next, we want to simplify the equation and solve for x.

Subtract x² from both sides: This eliminates the squared term, leaving us with: 6x  7 = 2x  3

Add 6x to both sides: This isolates the x term on the right side: 7 = 8x  3

Add 3 to both sides: This isolates the x term: 4 = 8x

Divide both sides by 8: This solves for x: x = 1/2
Conclusion
Therefore, the solution to the equation (x+1)(x7) = (x1)(x+3) is x = 1/2.
This means that if you substitute 1/2 for x in the original equation, both sides of the equation will be equal.