(x%2B5)%2B12%3D(x%2B3)(x-4)-2.jpeg "(x-2)(x+5)+12=(x+3)(x-4)-2")
Solving the Equation: (x-2)(x+5)+12=(x+3)(x-4)-2
In this article, we will solve the equation (x-2)(x+5)+12=(x+3)(x-4)-2. This equation involves multiplying binomials and simplifying expressions.
Step 1: Expand the Left Side of the Equation
Let's start by expanding the left side of the equation:
(x-2)(x+5) = x^2 + 3x - 10
Then, add 12 to both sides:
x^2 + 3x - 10 + 12 = x^2 + 3x + 2
Step 2: Expand the Right Side of the Equation
Now, let's expand the right side of the equation:
(x+3)(x-4) = x^2 - x - 12
Then, subtract 2 from both sides:
x^2 - x - 12 - 2 = x^2 - x - 14
Step 3: Equate the Two Expressions
Now that we have expanded both sides of the equation, we can equate them:
x^2 + 3x + 2 = x^2 - x - 14
Step 4: Simplify the Equation
Let's simplify the equation by combining like terms:
3x + 16 = -x - 12
Step 5: Solve for x
Now, let's solve for x:
4x = -28
x = -7
Therefore, the solution to the equation (x-2)(x+5)+12=(x+3)(x-4)-2 is x = -7.
