(3x-1)(2x+7)-(x+1)(6x-5)=(x+2)-(x-5)

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Jun 07, 2024

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Solving the Equation: (3x-1)(2x+7)-(x+1)(6x-5)=(x+2)-(x-5)

In this article, we will solve the equation (3x-1)(2x+7)-(x+1)(6x-5)=(x+2)-(x-5). This equation involves multiplying binomials and combining like terms.

Step 1: Multiply the Binomials

First, let's multiply the binomials:

(3x-1)(2x+7) = 6x^2 + 21x - 2x - 7 = 6x^2 + 19x - 7

(x+1)(6x-5) = 6x^2 - 5x + 6x - 5 = 6x^2 + x - 5

Now, we can rewrite the original equation as:

6x^2 + 19x - 7 - (6x^2 + x - 5) = x + 2 - (x - 5)

Step 2: Combine Like Terms

Next, we will combine like terms:

6x^2 + 19x - 7 - 6x^2 - x + 5 = x + 2 - x + 5

Simplifying the equation, we get:

18x - 2 = 7

Step 3: Solve for x

Finally, we can solve for x:

18x = 9

x = 9/18

x = 1/2

Therefore, the solution to the equation is x = 1/2.