(x%2B6)-(x-2)(x-3)%3D3.jpeg "(x-1)(x+6)-(x-2)(x-3)=3")
Solving the Equation: (x-1)(x+6)-(x-2)(x-3)=3
In this article, we will solve the given equation: (x-1)(x+6)-(x-2)(x-3)=3. To solve this equation, we will start by expanding the left-hand side of the equation and then simplify it to find the solution.
Expanding the Left-Hand Side
Let's expand the left-hand side of the equation:
(x-1)(x+6) = x^2 + 5x - 6
and
(x-2)(x-3) = x^2 - 5x + 6
Now, let's rewrite the equation by substituting these expressions:
x^2 + 5x - 6 - (x^2 - 5x + 6) = 3
Simplifying the Equation
Combine like terms:
10x - 12 = 3
Add 12 to both sides:
10x = 15
Divide by 10:
x = 1.5
Solution
Therefore, the solution to the equation (x-1)(x+6)-(x-2)(x-3)=3 is x = 1.5.
