(x-0.3)(x+0.5)=0

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Solution for (x-0.3)(x+0.5)=0 equation: 


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

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

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

Multiply (-0.3 + x) * (0.5 + x)
(-0.3(0.5 + x) + x(0.5 + x)) = 0
((0.5 * -0.3 + x * -0.3) + x(0.5 + x)) = 0
((-0.15 + -0.3x) + x(0.5 + x)) = 0
(-0.15 + -0.3x + (0.5 * x + x * x)) = 0
(-0.15 + -0.3x + (0.5x + x2)) = 0

Combine like terms: -0.3x + 0.5x = 0.2x
(-0.15 + 0.2x + x2) = 0

Solving
-0.15 + 0.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + 0.2x + 0.15 + x2 = 0 + 0.15

Reorder the terms:
-0.15 + 0.15 + 0.2x + x2 = 0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + 0.2x + x2 = 0 + 0.15
0.2x + x2 = 0 + 0.15

Combine like terms: 0 + 0.15 = 0.15
0.2x + x2 = 0.15

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 0.15 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 0.15 + 0.01

Combine like terms: 0.15 + 0.01 = 0.16
0.01 + 0.2x + x2 = 0.16

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 0.16

Calculate the square root of the right side: 0.4

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


Subproblem 1
x + 0.1 = 0.4

Simplifying
x + 0.1 = 0.4

Reorder the terms:
0.1 + x = 0.4

Solving
0.1 + x = 0.4

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 0.3


Subproblem 2
x + 0.1 = -0.4

Simplifying
x + 0.1 = -0.4

Reorder the terms:
0.1 + x = -0.4

Solving
0.1 + x = -0.4

Solving for variable 'x'.

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

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

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

Combine like terms: -0.4 + -0.1 = -0.5
x = -0.5

Simplifying
x = -0.5


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

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