(3m%2B10)%3D3(m%2B5)%2B15.jpeg "(m+2)(3m+10)=3(m+5)+15")
Solving the Equation (m+2)(3m+10) = 3(m+5) + 15
This article will guide you through the steps of solving the equation (m+2)(3m+10) = 3(m+5) + 15.
1. Expanding the Equation
First, we need to expand both sides of the equation by multiplying out the brackets.
- Left side: (m+2)(3m+10) = 3m² + 10m + 6m + 20 = 3m² + 16m + 20
- Right side: 3(m+5) + 15 = 3m + 15 + 15 = 3m + 30
Now, the equation becomes: 3m² + 16m + 20 = 3m + 30
2. Rearranging the Equation
Next, we want to bring all the terms to one side of the equation to make it easier to solve. We can do this by subtracting 3m and 30 from both sides:
3m² + 16m + 20 - 3m - 30 = 0
This simplifies to: 3m² + 13m - 10 = 0
3. Factoring the Quadratic Equation
Now we have a quadratic equation in the form of ax² + bx + c = 0. To solve it, we can factor the equation:
- Find factors of 3 (the coefficient of m²) and -10 (the constant term). The factors of 3 are 1 and 3, and the factors of -10 are 1, -1, 2, -2, 5, -5, 10, and -10.
- Find the combination of factors that adds up to 13 (the coefficient of m). In this case, the factors 15 and -2 satisfy this condition: 15 + (-2) = 13.
- Rewrite the equation using the factors. (3m - 2)(m + 5) = 0
4. Solving for m
The product of two factors is zero only if at least one of them is zero. Therefore, we have two possible solutions:
- 3m - 2 = 0 => 3m = 2 => m = 2/3
- m + 5 = 0 => m = -5
Conclusion
The solutions to the equation (m+2)(3m+10) = 3(m+5) + 15 are m = 2/3 and m = -5.