(a-0.3)(a-0.5)=

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Solution for (a-0.3)(a-0.5)= equation: 


Simplifying
(a + -0.3)(a + -0.5) = 0

Reorder the terms:
(-0.3 + a)(a + -0.5) = 0

Reorder the terms:
(-0.3 + a)(-0.5 + a) = 0

Multiply (-0.3 + a) * (-0.5 + a)
(-0.3(-0.5 + a) + a(-0.5 + a)) = 0
((-0.5 * -0.3 + a * -0.3) + a(-0.5 + a)) = 0
((0.15 + -0.3a) + a(-0.5 + a)) = 0
(0.15 + -0.3a + (-0.5 * a + a * a)) = 0
(0.15 + -0.3a + (-0.5a + a2)) = 0

Combine like terms: -0.3a + -0.5a = -0.8a
(0.15 + -0.8a + a2) = 0

Solving
0.15 + -0.8a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-0.15' to each side of the equation.
0.15 + -0.8a + -0.15 + a2 = 0 + -0.15

Reorder the terms:
0.15 + -0.15 + -0.8a + a2 = 0 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + -0.8a + a2 = 0 + -0.15
-0.8a + a2 = 0 + -0.15

Combine like terms: 0 + -0.15 = -0.15
-0.8a + a2 = -0.15

The a term is -0.8a.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8a + 0.16 + a2 = -0.15 + 0.16

Reorder the terms:
0.16 + -0.8a + a2 = -0.15 + 0.16

Combine like terms: -0.15 + 0.16 = 0.01
0.16 + -0.8a + a2 = 0.01

Factor a perfect square on the left side:
(a + -0.4)(a + -0.4) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(a + -0.4) equal to 0.1 and -0.1.


Subproblem 1
a + -0.4 = 0.1

Simplifying
a + -0.4 = 0.1

Reorder the terms:
-0.4 + a = 0.1

Solving
-0.4 + a = 0.1

Solving for variable 'a'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + a = 0.1 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + a = 0.1 + 0.4
a = 0.1 + 0.4

Combine like terms: 0.1 + 0.4 = 0.5
a = 0.5

Simplifying
a = 0.5


Subproblem 2
a + -0.4 = -0.1

Simplifying
a + -0.4 = -0.1

Reorder the terms:
-0.4 + a = -0.1

Solving
-0.4 + a = -0.1

Solving for variable 'a'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + a = -0.1 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + a = -0.1 + 0.4
a = -0.1 + 0.4

Combine like terms: -0.1 + 0.4 = 0.3
a = 0.3

Simplifying
a = 0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.5, 0.3}

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