0.3a(0.2a+0.5)+0.2(a+2)=1.3

Solution for 0.3a(0.2a+0.5)+0.2(a+2)=1.3 equation:

Simplifying
0.3a(0.2a + 0.5) + 0.2(a + 2) = 1.3

Reorder the terms:
0.3a(0.5 + 0.2a) + 0.2(a + 2) = 1.3
(0.5 * 0.3a + 0.2a * 0.3a) + 0.2(a + 2) = 1.3
(0.15a + 0.06a2) + 0.2(a + 2) = 1.3

Reorder the terms:
0.15a + 0.06a2 + 0.2(2 + a) = 1.3
0.15a + 0.06a2 + (2 * 0.2 + a * 0.2) = 1.3
0.15a + 0.06a2 + (0.4 + 0.2a) = 1.3

Reorder the terms:
0.4 + 0.15a + 0.2a + 0.06a2 = 1.3

Combine like terms: 0.15a + 0.2a = 0.35a
0.4 + 0.35a + 0.06a2 = 1.3

Solving
0.4 + 0.35a + 0.06a2 = 1.3

Solving for variable 'a'.

Reorder the terms:
0.4 + -1.3 + 0.35a + 0.06a2 = 1.3 + -1.3

Combine like terms: 0.4 + -1.3 = -0.9
-0.9 + 0.35a + 0.06a2 = 1.3 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
-0.9 + 0.35a + 0.06a2 = 0.0

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

Divide each side by '0.06'.
-15 + 5.833333333a + a2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 5.833333333a + 15 + a2 = 0 + 15

Reorder the terms:
-15 + 15 + 5.833333333a + a2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 5.833333333a + a2 = 0 + 15
5.833333333a + a2 = 0 + 15

Combine like terms: 0 + 15 = 15
5.833333333a + a2 = 15

The a term is 5.833333333a.  Take half its coefficient (2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
5.833333333a + 8.506944446 + a2 = 15 + 8.506944446

Reorder the terms:
8.506944446 + 5.833333333a + a2 = 15 + 8.506944446

Combine like terms: 15 + 8.506944446 = 23.506944446
8.506944446 + 5.833333333a + a2 = 23.506944446

Factor a perfect square on the left side:
(a + 2.916666667)(a + 2.916666667) = 23.506944446

Calculate the square root of the right side: 4.848396069

Break this problem into two subproblems by setting 
(a + 2.916666667) equal to 4.848396069 and -4.848396069.

Subproblem 1
a + 2.916666667 = 4.848396069

Simplifying
a + 2.916666667 = 4.848396069

Reorder the terms:
2.916666667 + a = 4.848396069

Solving
2.916666667 + a = 4.848396069

Solving for variable 'a'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + a = 4.848396069 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + a = 4.848396069 + -2.916666667
a = 4.848396069 + -2.916666667

Combine like terms: 4.848396069 + -2.916666667 = 1.931729402
a = 1.931729402

Simplifying
a = 1.931729402

Subproblem 2
a + 2.916666667 = -4.848396069

Simplifying
a + 2.916666667 = -4.848396069

Reorder the terms:
2.916666667 + a = -4.848396069

Solving
2.916666667 + a = -4.848396069

Solving for variable 'a'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + a = -4.848396069 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + a = -4.848396069 + -2.916666667
a = -4.848396069 + -2.916666667

Combine like terms: -4.848396069 + -2.916666667 = -7.765062736
a = -7.765062736

Simplifying
a = -7.765062736

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.931729402, -7.765062736}