(x%2B3)%3D(x%2B5)(x-4).jpeg "(x-1)(x+3)=(x+5)(x-4)")
Solving the Equation: (x-1)(x+3)=(x+5)(x-4)
In this article, we will solve the equation (x-1)(x+3)=(x+5)(x-4) and find the values of x that satisfy the equation.
Step 1: Expand the Left-Hand Side
Using the distributive property of multiplication over addition, we can expand the left-hand side of the equation as follows:
(x-1)(x+3) = x^2 + 2x - 3
Step 2: Expand the Right-Hand Side
Similarly, we can expand the right-hand side of the equation as follows:
(x+5)(x-4) = x^2 + x - 20
Step 3: Equate the Two Expressions
Now, we can equate the two expressions and solve for x:
x^2 + 2x - 3 = x^2 + x - 20
Step 4: Simplify the Equation
Subtract x^2 from both sides of the equation to eliminate the x^2 term:
2x - 3 = x - 20
Step 5: Solve for x
Add 3 to both sides of the equation to get:
2x = x - 17
Subtract x from both sides to get:
x = -17
Therefore, the solution to the equation (x-1)(x+3)=(x+5)(x-4) is x = -17.
Conclusion
In this article, we have solved the equation (x-1)(x+3)=(x+5)(x-4) and found the solution to be x = -17.
