%5E2-(4x-3)(3x%2B1)%3D6(2x-5)%5E2%2B113x.jpeg "(6x-1)^2-(4x-3)(3x+1)=6(2x-5)^2+113x")
Solving the Equation (6x-1)^2-(4x-3)(3x+1)=6(2x-5)^2+113x
This article will guide you through the steps to solve the equation:
(6x-1)^2-(4x-3)(3x+1)=6(2x-5)^2+113x
Let's break it down step by step:
1. Expand the squares and products
First, we need to expand all the squares and products in the equation:
- (6x-1)^2 = (6x-1)(6x-1) = 36x^2 - 12x + 1
- (4x-3)(3x+1) = 12x^2 - 5x - 3
- 6(2x-5)^2 = 6(2x-5)(2x-5) = 24x^2 - 120x + 150
Now, our equation becomes:
36x^2 - 12x + 1 - (12x^2 - 5x - 3) = 24x^2 - 120x + 150 + 113x
2. Simplify the equation
Next, we simplify the equation by removing the parentheses and combining like terms:
36x^2 - 12x + 1 - 12x^2 + 5x + 3 = 24x^2 - 120x + 150 + 113x
This simplifies to:
24x^2 - 7x + 4 = 24x^2 - 7x + 150
3. Solve for x
We can see that both sides of the equation have the same terms, except for the constant terms. Therefore, the equation will not have a unique solution for x. We can write the solution as:
24x^2 - 7x + 4 = 24x^2 - 7x + 150
This equation has no solution.
Conclusion
The equation (6x-1)^2-(4x-3)(3x+1)=6(2x-5)^2+113x has no solution. This is because the terms on both sides of the equation simplify to the same terms, except for the constant terms.