(3x-1)(4x+5)-(2x+3)(6x+1)=4

2 min read Jun 16, 2024

Solving the Equation: (3x-1)(4x+5)-(2x+3)(6x+1)=4

This article will guide you through solving the algebraic equation: (3x-1)(4x+5)-(2x+3)(6x+1)=4. We'll break down the process step-by-step, ensuring you understand each stage.

1. Expanding the Products

First, we need to expand the products on both sides of the equation using the FOIL method (First, Outer, Inner, Last).

(3x-1)(4x+5):
- First: (3x)(4x) = 12x²
- Outer: (3x)(5) = 15x
- Inner: (-1)(4x) = -4x
- Last: (-1)(5) = -5
- Combined: 12x² + 15x - 4x - 5 = 12x² + 11x - 5
(2x+3)(6x+1):
- First: (2x)(6x) = 12x²
- Outer: (2x)(1) = 2x
- Inner: (3)(6x) = 18x
- Last: (3)(1) = 3
- Combined: 12x² + 2x + 18x + 3 = 12x² + 20x + 3

Now our equation looks like this: 12x² + 11x - 5 - (12x² + 20x + 3) = 4

2. Simplifying the Equation

Next, we can simplify the equation by distributing the negative sign and combining like terms:

12x² + 11x - 5 - 12x² - 20x - 3 = 4
-9x - 8 = 4

3. Isolating the Variable

To isolate the variable 'x', we need to move all the constant terms to the right side of the equation:

-9x = 4 + 8
-9x = 12

4. Solving for x

Finally, divide both sides by -9 to find the value of 'x':

x = 12 / -9
x = -4/3

Therefore, the solution to the equation (3x-1)(4x+5)-(2x+3)(6x+1)=4 is x = -4/3.