(2x%2B4)%2B(4x-1)(5-3x)%3D-21.jpeg "(6x-3)(2x+4)+(4x-1)(5-3x)=-21")
Solving the Equation: (6x-3)(2x+4)+(4x-1)(5-3x) = -21
This article will guide you through the steps to solve the equation: (6x-3)(2x+4)+(4x-1)(5-3x) = -21.
Step 1: Expand the Products
First, we need to expand the products on the left-hand side of the equation using the distributive property (or FOIL method).
- (6x-3)(2x+4) = 12x² + 24x - 6x - 12 = 12x² + 18x - 12
- (4x-1)(5-3x) = 20x - 12x² - 5 + 3x = -12x² + 23x - 5
Now our equation becomes: 12x² + 18x - 12 - 12x² + 23x - 5 = -21
Step 2: Simplify the Equation
Next, combine the like terms on the left-hand side of the equation:
41x - 17 = -21
Step 3: Isolate the Variable
To isolate the variable (x), add 17 to both sides of the equation:
41x = -4
Step 4: Solve for x
Finally, divide both sides of the equation by 41 to get the value of x:
x = -4/41
Conclusion
Therefore, the solution to the equation (6x-3)(2x+4)+(4x-1)(5-3x) = -21 is x = -4/41.