Solving the Equation: (x+3)(x7)(x4)(x+4)=11
This article will guide you through the steps of solving the equation (x+3)(x7)(x4)(x+4)=11.
Expanding the Equation
First, we need to expand the equation by multiplying the terms in the brackets. We'll use the FOIL method (First, Outer, Inner, Last) for this:

(x+3)(x7):
 First: x * x = x²
 Outer: x * 7 = 7x
 Inner: 3 * x = 3x
 Last: 3 * 7 = 21
 Combining terms: x²  7x + 3x  21 = x²  4x  21

(x4)(x+4):
 First: x * x = x²
 Outer: x * 4 = 4x
 Inner: 4 * x = 4x
 Last: 4 * 4 = 16
 Combining terms: x² + 4x  4x  16 = x²  16
Now, we can substitute these expanded terms back into the original equation:
(x²  4x  21)  (x²  16) = 11
Simplifying the Equation
Next, we'll simplify the equation by removing the brackets and combining like terms:
x²  4x  21  x² + 16 = 11
4x  5 = 11
Isolating the Variable
Our goal is to isolate the variable 'x'. We start by moving the constant term to the right side of the equation:
4x = 11 + 5
4x = 16
Solving for x
Finally, we divide both sides of the equation by 4 to solve for 'x':
x = 16 / 4
x = 4
Conclusion
Therefore, the solution to the equation (x+3)(x7)(x4)(x+4)=11 is x = 4.