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

Jasonbradley

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Jun 16, 2024

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

This article will guide you through solving the equation (x+2)(x-3)+6=x(x+5). We'll break down the steps involved, simplifying the equation and ultimately finding the value of 'x'.

Expanding the Equation

First, we need to expand both sides of the equation to get rid of the parentheses.

• Left Side:

  • (x+2)(x-3) = x² - x - 6 (using FOIL method)
  • (x² - x - 6) + 6 = x² - x

• Right Side:

  • x(x+5) = x² + 5x

Now, the equation becomes: x² - x = x² + 5x

Simplifying and Solving

Next, we simplify the equation by moving all the terms to one side.

• Subtracting x² from both sides: -x = 5x
• Subtracting 5x from both sides: -6x = 0
• Dividing both sides by -6: x = 0

Solution

Therefore, the solution to the equation (x+2)(x-3)+6=x(x+5) is x = 0.

To verify our solution, we can substitute x = 0 back into the original equation:

• (0 + 2)(0 - 3) + 6 = 0(0 + 5)
• (2)(-3) + 6 = 0
• -6 + 6 = 0
• 0 = 0

Since the equation holds true, we've confirmed that our solution, x = 0, is correct.