Solving the Equation: (m+5)(3m+4) = 3(m+2)  2
This article will guide you through the process of solving the equation (m+5)(3m+4) = 3(m+2)  2. We will use algebraic techniques to isolate the variable 'm' and find its solution.
Step 1: Expand Both Sides of the Equation
First, we need to expand both sides of the equation to simplify them.
 Left Side: (m+5)(3m+4) = 3m² + 19m + 20
 Right Side: 3(m+2)  2 = 3m + 6  2 = 3m + 4
Now the equation becomes: 3m² + 19m + 20 = 3m + 4
Step 2: Move All Terms to One Side
To solve for 'm', we need to have all the terms on one side of the equation. Subtract 3m and 4 from both sides.
3m² + 19m + 20  3m  4 = 0
This simplifies to: 3m² + 16m + 16 = 0
Step 3: Factor the Quadratic Equation
The equation is now a quadratic equation in the form of ax² + bx + c = 0. To solve it, we need to factor it.
 Factorization: (3m + 8)(m + 2) = 0
Step 4: Solve for 'm'
To find the solutions for 'm', set each factor equal to zero and solve.

3m + 8 = 0
 3m = 8
 m = 8/3

m + 2 = 0
 m = 2
Solution
Therefore, the solutions to the equation (m+5)(3m+4) = 3(m+2)  2 are:
 m = 8/3
 m = 2