a*(2a+4)=2+3a

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

Simplifying
a(2a + 4) = 2 + 3a

Reorder the terms:
a(4 + 2a) = 2 + 3a
(4 * a + 2a * a) = 2 + 3a
(4a + 2a2) = 2 + 3a

Solving
4a + 2a2 = 2 + 3a

Solving for variable 'a'.

Reorder the terms:
-2 + 4a + -3a + 2a2 = 2 + 3a + -2 + -3a

Combine like terms: 4a + -3a = 1a
-2 + 1a + 2a2 = 2 + 3a + -2 + -3a

Reorder the terms:
-2 + 1a + 2a2 = 2 + -2 + 3a + -3a

Combine like terms: 2 + -2 = 0
-2 + 1a + 2a2 = 0 + 3a + -3a
-2 + 1a + 2a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-2 + 1a + 2a2 = 0

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

Divide each side by '2'.
-1 + 0.5a + a2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.5a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.5a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.5a + a2 = 0 + 1
0.5a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.5a + a2 = 1

The a term is 0.5a.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5a + 0.0625 + a2 = 1 + 0.0625

Reorder the terms:
0.0625 + 0.5a + a2 = 1 + 0.0625

Combine like terms: 1 + 0.0625 = 1.0625
0.0625 + 0.5a + a2 = 1.0625

Factor a perfect square on the left side:
(a + 0.25)(a + 0.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(a + 0.25) equal to 1.030776406 and -1.030776406.

Subproblem 1
a + 0.25 = 1.030776406

Simplifying
a + 0.25 = 1.030776406

Reorder the terms:
0.25 + a = 1.030776406

Solving
0.25 + a = 1.030776406

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = 1.030776406 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = 1.030776406 + -0.25
a = 1.030776406 + -0.25

Combine like terms: 1.030776406 + -0.25 = 0.780776406
a = 0.780776406

Simplifying
a = 0.780776406

Subproblem 2
a + 0.25 = -1.030776406

Simplifying
a + 0.25 = -1.030776406

Reorder the terms:
0.25 + a = -1.030776406

Solving
0.25 + a = -1.030776406

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = -1.030776406 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = -1.030776406 + -0.25
a = -1.030776406 + -0.25

Combine like terms: -1.030776406 + -0.25 = -1.280776406
a = -1.280776406

Simplifying
a = -1.280776406

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.780776406, -1.280776406}