Solving the Equation (m+4)(4m2) = 5(m+3)  10
This article will guide you through the process of solving the equation (m+4)(4m2) = 5(m+3)  10.
Step 1: Expand the equation
First, we need to expand both sides of the equation by using the distributive property:
 Left side: (m+4)(4m2) = 4m²  2m + 16m  8 = 4m² + 14m  8
 Right side: 5(m+3)  10 = 5m + 15  10 = 5m + 5
Now our equation looks like this: 4m² + 14m  8 = 5m + 5
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. Let's subtract 5m and 5 from both sides:
4m² + 14m  8  5m  5 = 0
This simplifies to: 4m² + 9m  13 = 0
Step 3: Solve the quadratic equation
Now we have a quadratic equation. There are a few ways to solve it:

Factoring: Try to factor the quadratic expression. However, in this case, factoring might not be straightforward.

Quadratic Formula: The quadratic formula is a reliable method to find the solutions of any quadratic equation. The formula is:
m = (b ± √(b²  4ac)) / 2a
Where a, b, and c are the coefficients of the quadratic equation (ax² + bx + c = 0).
In our equation, a = 4, b = 9, and c = 13. Substitute these values into the quadratic formula and solve for m.

Completing the Square: This method involves manipulating the equation to create a perfect square trinomial. However, it's usually less efficient than the quadratic formula for this particular equation.
Step 4: Find the solutions
After applying the quadratic formula (or your preferred method), you'll get two solutions for m. These solutions represent the values of m that make the original equation true.
Conclusion
By following these steps, you can solve the equation (m+4)(4m2) = 5(m+3)  10 and find the values of m that satisfy the equation. Remember to doublecheck your solutions by plugging them back into the original equation.