4(a+2)2a=10+3(a-3)

Solution for 4(a+2)2a=10+3(a-3) equation:

Simplifying
4(a + 2) * 2a = 10 + 3(a + -3)

Reorder the terms:
4(2 + a) * 2a = 10 + 3(a + -3)

Reorder the terms for easier multiplication:
4 * 2a(2 + a) = 10 + 3(a + -3)

Multiply 4 * 2
8a(2 + a) = 10 + 3(a + -3)
(2 * 8a + a * 8a) = 10 + 3(a + -3)
(16a + 8a2) = 10 + 3(a + -3)

Reorder the terms:
16a + 8a2 = 10 + 3(-3 + a)
16a + 8a2 = 10 + (-3 * 3 + a * 3)
16a + 8a2 = 10 + (-9 + 3a)

Combine like terms: 10 + -9 = 1
16a + 8a2 = 1 + 3a

Solving
16a + 8a2 = 1 + 3a

Solving for variable 'a'.

Reorder the terms:
-1 + 16a + -3a + 8a2 = 1 + 3a + -1 + -3a

Combine like terms: 16a + -3a = 13a
-1 + 13a + 8a2 = 1 + 3a + -1 + -3a

Reorder the terms:
-1 + 13a + 8a2 = 1 + -1 + 3a + -3a

Combine like terms: 1 + -1 = 0
-1 + 13a + 8a2 = 0 + 3a + -3a
-1 + 13a + 8a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-1 + 13a + 8a2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-0.125 + 1.625a + a2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 1.625a + 0.125 + a2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 1.625a + a2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 1.625a + a2 = 0 + 0.125
1.625a + a2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
1.625a + a2 = 0.125

The a term is 1.625a.  Take half its coefficient (0.8125).
Square it (0.66015625) and add it to both sides.

Add '0.66015625' to each side of the equation.
1.625a + 0.66015625 + a2 = 0.125 + 0.66015625

Reorder the terms:
0.66015625 + 1.625a + a2 = 0.125 + 0.66015625

Combine like terms: 0.125 + 0.66015625 = 0.78515625
0.66015625 + 1.625a + a2 = 0.78515625

Factor a perfect square on the left side:
(a + 0.8125)(a + 0.8125) = 0.78515625

Calculate the square root of the right side: 0.88609043

Break this problem into two subproblems by setting 
(a + 0.8125) equal to 0.88609043 and -0.88609043.

Subproblem 1
a + 0.8125 = 0.88609043

Simplifying
a + 0.8125 = 0.88609043

Reorder the terms:
0.8125 + a = 0.88609043

Solving
0.8125 + a = 0.88609043

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.8125' to each side of the equation.
0.8125 + -0.8125 + a = 0.88609043 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + a = 0.88609043 + -0.8125
a = 0.88609043 + -0.8125

Combine like terms: 0.88609043 + -0.8125 = 0.07359043
a = 0.07359043

Simplifying
a = 0.07359043

Subproblem 2
a + 0.8125 = -0.88609043

Simplifying
a + 0.8125 = -0.88609043

Reorder the terms:
0.8125 + a = -0.88609043

Solving
0.8125 + a = -0.88609043

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.8125' to each side of the equation.
0.8125 + -0.8125 + a = -0.88609043 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + a = -0.88609043 + -0.8125
a = -0.88609043 + -0.8125

Combine like terms: -0.88609043 + -0.8125 = -1.69859043
a = -1.69859043

Simplifying
a = -1.69859043

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.07359043, -1.69859043}