(m-4)(3m-10)=3(m-2)+18

3 min read Jun 16, 2024

Solving the Equation: (m-4)(3m-10) = 3(m-2) + 18

This article will guide you through the steps of solving the equation (m-4)(3m-10) = 3(m-2) + 18. We will use algebraic manipulations to isolate the variable m and find its value.

Step 1: Expand both sides of the equation

First, we need to expand the products on both sides of the equation.

Left side: (m-4)(3m-10) = 3m² - 10m - 12m + 40 = 3m² - 22m + 40
Right side: 3(m-2) + 18 = 3m - 6 + 18 = 3m + 12

Now the equation becomes: 3m² - 22m + 40 = 3m + 12

Step 2: Move all terms to one side

To solve for m, we need to have a quadratic equation (an equation with a term containing m²). To achieve this, subtract 3m + 12 from both sides:

3m² - 22m + 40 - (3m + 12) = 0

Simplifying the equation, we get: 3m² - 25m + 28 = 0

Step 3: Factor the quadratic equation

Now we need to factor the quadratic equation. We can factor it as follows:

(3m - 4)(m - 7) = 0

Step 4: Solve for m

For the product of two factors to be zero, at least one of them must be zero. Therefore, we have two possible solutions:

3m - 4 = 0
- Adding 4 to both sides: 3m = 4
- Dividing both sides by 3: m = 4/3
m - 7 = 0
- Adding 7 to both sides: m = 7

Conclusion

The solutions to the equation (m-4)(3m-10) = 3(m-2) + 18 are m = 4/3 and m = 7.