(0.2a+1.3)(0.5a-0.1)=

Solution for (0.2a+1.3)(0.5a-0.1)= equation:

Simplifying
(0.2a + 1.3)(0.5a + -0.1) = 0

Reorder the terms:
(1.3 + 0.2a)(0.5a + -0.1) = 0

Reorder the terms:
(1.3 + 0.2a)(-0.1 + 0.5a) = 0

Multiply (1.3 + 0.2a) * (-0.1 + 0.5a)
(1.3(-0.1 + 0.5a) + 0.2a * (-0.1 + 0.5a)) = 0
((-0.1 * 1.3 + 0.5a * 1.3) + 0.2a * (-0.1 + 0.5a)) = 0
((-0.13 + 0.65a) + 0.2a * (-0.1 + 0.5a)) = 0
(-0.13 + 0.65a + (-0.1 * 0.2a + 0.5a * 0.2a)) = 0
(-0.13 + 0.65a + (-0.02a + 0.1a2)) = 0

Combine like terms: 0.65a + -0.02a = 0.63a
(-0.13 + 0.63a + 0.1a2) = 0

Solving
-0.13 + 0.63a + 0.1a2 = 0

Solving for variable 'a'.

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

Divide each side by '0.1'.
-1.3 + 6.3a + a2 = 0

Move the constant term to the right:

Add '1.3' to each side of the equation.
-1.3 + 6.3a + 1.3 + a2 = 0 + 1.3

Reorder the terms:
-1.3 + 1.3 + 6.3a + a2 = 0 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + 6.3a + a2 = 0 + 1.3
6.3a + a2 = 0 + 1.3

Combine like terms: 0 + 1.3 = 1.3
6.3a + a2 = 1.3

The a term is 6.3a.  Take half its coefficient (3.15).
Square it (9.9225) and add it to both sides.

Add '9.9225' to each side of the equation.
6.3a + 9.9225 + a2 = 1.3 + 9.9225

Reorder the terms:
9.9225 + 6.3a + a2 = 1.3 + 9.9225

Combine like terms: 1.3 + 9.9225 = 11.2225
9.9225 + 6.3a + a2 = 11.2225

Factor a perfect square on the left side:
(a + 3.15)(a + 3.15) = 11.2225

Calculate the square root of the right side: 3.35

Break this problem into two subproblems by setting 
(a + 3.15) equal to 3.35 and -3.35.

Subproblem 1
a + 3.15 = 3.35

Simplifying
a + 3.15 = 3.35

Reorder the terms:
3.15 + a = 3.35

Solving
3.15 + a = 3.35

Solving for variable 'a'.

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

Add '-3.15' to each side of the equation.
3.15 + -3.15 + a = 3.35 + -3.15

Combine like terms: 3.15 + -3.15 = 0.00
0.00 + a = 3.35 + -3.15
a = 3.35 + -3.15

Combine like terms: 3.35 + -3.15 = 0.2
a = 0.2

Simplifying
a = 0.2

Subproblem 2
a + 3.15 = -3.35

Simplifying
a + 3.15 = -3.35

Reorder the terms:
3.15 + a = -3.35

Solving
3.15 + a = -3.35

Solving for variable 'a'.

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

Add '-3.15' to each side of the equation.
3.15 + -3.15 + a = -3.35 + -3.15

Combine like terms: 3.15 + -3.15 = 0.00
0.00 + a = -3.35 + -3.15
a = -3.35 + -3.15

Combine like terms: -3.35 + -3.15 = -6.5
a = -6.5

Simplifying
a = -6.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.2, -6.5}