Solving the Equation: (53a)(4a+6)=(8a+1)3(2a+3)
This article will guide you through the steps of solving the equation (53a)(4a+6)=(8a+1)3(2a+3). Let's break it down step by step:
1. Simplifying Both Sides
First, we need to simplify both sides of the equation by removing the parentheses.
 Left Side:
 Distribute the negative sign: (5  3a) + (4a  6)
 Combine like terms: a  1
 Right Side:
 Distribute the 3: (8a + 1)  (6a + 9)
 Combine like terms: 2a  8
Now, the equation is simplified to: a  1 = 2a  8
2. Isolating the Variable
Next, we need to isolate the variable a on one side of the equation. We can achieve this by:

Subtracting a from both sides:
 (a  1)  a = (2a  8)  a
 This simplifies to: 1 = a  8

Adding 8 to both sides:
 (1) + 8 = (a  8) + 8
 This simplifies to: 7 = a
3. Solution
Therefore, the solution to the equation (53a)(4a+6)=(8a+1)3(2a+3) is a = 7.
4. Verification
To verify our solution, we can substitute a = 7 back into the original equation:
(5  3(7))  (4(7) + 6) = (8(7) + 1)  3(2(7) + 3)
 Simplifying both sides:
 (16)  (22) = (57)  (48)
 6 = 9
Since both sides of the equation are equal after substituting a = 7, our solution is verified.