(2x-3)(5x+7)=10x(x-3)+37

2 min read Jun 16, 2024

Solving the Equation: (2x-3)(5x+7) = 10x(x-3) + 37

This article will guide you through the process of solving the equation (2x-3)(5x+7) = 10x(x-3) + 37. We will use algebraic manipulation to simplify the equation and ultimately find the values of x that satisfy the equation.

Step 1: Expanding the Products

First, we expand the products on both sides of the equation:

Left side: (2x-3)(5x+7) = 10x² + 14x - 15x - 21 = 10x² - x - 21
Right side: 10x(x-3) + 37 = 10x² - 30x + 37

Now our equation becomes: 10x² - x - 21 = 10x² - 30x + 37

Step 2: Simplifying the Equation

We can simplify the equation by subtracting 10x² from both sides, which eliminates the quadratic term:

-x - 21 = -30x + 37

Step 3: Isolating the Variable

Next, we isolate the x term by adding 30x to both sides:

29x - 21 = 37

Step 4: Solving for x

Finally, we solve for x by adding 21 to both sides and then dividing by 29:

29x = 58

x = 58/29

x = 2

Conclusion

Therefore, the solution to the equation (2x-3)(5x+7) = 10x(x-3) + 37 is x = 2. We can verify this solution by substituting x = 2 back into the original equation and confirming that both sides are equal.