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

2 min read Jun 16, 2024
(3x-1)(4x+5)-(2x+3)(6x+1)=4

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.

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