(2x+5)(6x-1)=120 Solve For X

Jasonbradley

2 min read

·

Jun 16, 2024

28

Share

Solving the Equation (2x+5)(6x-1) = 120

This equation involves a product of two binomials set equal to a constant. To solve for x, we need to follow these steps:

1. Expand the product:

• Use the FOIL method (First, Outer, Inner, Last) to multiply the binomials:
  • (2x+5)(6x-1) = (2x * 6x) + (2x * -1) + (5 * 6x) + (5 * -1)
  • (2x+5)(6x-1) = 12x² - 2x + 30x - 5
  • (2x+5)(6x-1) = 12x² + 28x - 5

2. Rearrange the equation:

• Move all terms to one side to set the equation equal to zero:
  • 12x² + 28x - 5 - 120 = 0
  • 12x² + 28x - 125 = 0

3. Solve the quadratic equation:

• We can solve this quadratic equation using the quadratic formula:
  • x = (-b ± √(b² - 4ac)) / 2a
  • Where a = 12, b = 28, and c = -125

4. Substitute the values and simplify:

• x = (-28 ± √(28² - 4 * 12 * -125)) / (2 * 12)
• x = (-28 ± √(784 + 6000)) / 24
• x = (-28 ± √6784) / 24
• x = (-28 ± 82) / 24

5. Calculate the solutions:

• x1 = (-28 + 82) / 24 = 54 / 24 = 9/4
• x2 = (-28 - 82) / 24 = -110 / 24 = -55/12

Therefore, the solutions for the equation (2x+5)(6x-1) = 120 are x = 9/4 and x = -55/12.