(m+5)(3m+4)=3(m+2)-2

2 min read Jun 16, 2024

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