Solve the Linear Equation: 16a-20a+15=2(5-2a)

Let's solve the problem step-by-step:

Step 1: Begin with the original equation:
$16a - 20a + 15 = 2(5 - 2a)$.

Step 2: Simplify the left-hand side by combining like terms:
$16a - 20a + 15 = -4a + 15$.

Step 3: Apply the distributive property to the right-hand side:
$2(5 - 2a) = 2 \cdot 5 - 2 \cdot 2a = 10 - 4a$.

Step 4: Now the equation reads:
$-4a + 15 = 10 - 4a$.

Step 5: Attempt to isolate the variable $a$ by subtracting $10$ from both sides:
$-4a + 15 - 10 = -4a$.
This simplifies to:
$-4a + 5 = -4a$.

Step 6: Subtract $-4a$ from both sides to further simplify the equation:
$5 = 0$.
This is a contradiction, indicating that no solution exists for the equation since a statement like this is never true.

Therefore, the solution to the problem is No solution.