## 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.