(x%2B3)-(2x-1)(3x-1)%3D0.jpeg "(2x-1)(x+3)-(2x-1)(3x-1)=0")
Solving the Equation: (2x-1)(x+3)-(2x-1)(3x-1)=0
This equation presents a straightforward example of factoring and solving a quadratic equation. Let's break down the steps to find the solution.
1. Factoring out the common term
Notice that both terms on the left side of the equation share a common factor of (2x-1). We can factor this out:
(2x-1)(x+3) - (2x-1)(3x-1) = 0
(2x-1)[(x+3)-(3x-1)] = 0
2. Simplifying the expression
Now, we simplify the expression inside the brackets:
(2x-1)(-2x+4) = 0
3. Setting each factor to zero
For the product of two factors to be zero, at least one of them must be zero. Therefore, we set each factor equal to zero and solve for x:
(2x-1) = 0 or (-2x+4) = 0
4. Solving for x
Solving each equation:
- 2x - 1 = 0 --> x = 1/2
- -2x + 4 = 0 --> x = 2
Conclusion
Therefore, the solutions to the equation (2x-1)(x+3)-(2x-1)(3x-1)=0 are x = 1/2 and x = 2.