(0.2x-0.3)(0.04x+3)=0

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Solution for (0.2x-0.3)(0.04x+3)=0 equation: 


Simplifying
(0.2x + -0.3)(0.04x + 3) = 0

Reorder the terms:
(-0.3 + 0.2x)(0.04x + 3) = 0

Reorder the terms:
(-0.3 + 0.2x)(3 + 0.04x) = 0

Multiply (-0.3 + 0.2x) * (3 + 0.04x)
(-0.3(3 + 0.04x) + 0.2x * (3 + 0.04x)) = 0
((3 * -0.3 + 0.04x * -0.3) + 0.2x * (3 + 0.04x)) = 0
((-0.9 + -0.012x) + 0.2x * (3 + 0.04x)) = 0
(-0.9 + -0.012x + (3 * 0.2x + 0.04x * 0.2x)) = 0
(-0.9 + -0.012x + (0.6x + 0.008x2)) = 0

Combine like terms: -0.012x + 0.6x = 0.588x
(-0.9 + 0.588x + 0.008x2) = 0

Solving
-0.9 + 0.588x + 0.008x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.008'.
-112.5 + 73.5x + x2 = 0

Move the constant term to the right:

Add '112.5' to each side of the equation.
-112.5 + 73.5x + 112.5 + x2 = 0 + 112.5

Reorder the terms:
-112.5 + 112.5 + 73.5x + x2 = 0 + 112.5

Combine like terms: -112.5 + 112.5 = 0.0
0.0 + 73.5x + x2 = 0 + 112.5
73.5x + x2 = 0 + 112.5

Combine like terms: 0 + 112.5 = 112.5
73.5x + x2 = 112.5

The x term is 73.5x.  Take half its coefficient (36.75).
Square it (1350.5625) and add it to both sides.

Add '1350.5625' to each side of the equation.
73.5x + 1350.5625 + x2 = 112.5 + 1350.5625

Reorder the terms:
1350.5625 + 73.5x + x2 = 112.5 + 1350.5625

Combine like terms: 112.5 + 1350.5625 = 1463.0625
1350.5625 + 73.5x + x2 = 1463.0625

Factor a perfect square on the left side:
(x + 36.75)(x + 36.75) = 1463.0625

Calculate the square root of the right side: 38.25

Break this problem into two subproblems by setting 
(x + 36.75) equal to 38.25 and -38.25.


Subproblem 1
x + 36.75 = 38.25

Simplifying
x + 36.75 = 38.25

Reorder the terms:
36.75 + x = 38.25

Solving
36.75 + x = 38.25

Solving for variable 'x'.

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

Add '-36.75' to each side of the equation.
36.75 + -36.75 + x = 38.25 + -36.75

Combine like terms: 36.75 + -36.75 = 0.00
0.00 + x = 38.25 + -36.75
x = 38.25 + -36.75

Combine like terms: 38.25 + -36.75 = 1.5
x = 1.5

Simplifying
x = 1.5


Subproblem 2
x + 36.75 = -38.25

Simplifying
x + 36.75 = -38.25

Reorder the terms:
36.75 + x = -38.25

Solving
36.75 + x = -38.25

Solving for variable 'x'.

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

Add '-36.75' to each side of the equation.
36.75 + -36.75 + x = -38.25 + -36.75

Combine like terms: 36.75 + -36.75 = 0.00
0.00 + x = -38.25 + -36.75
x = -38.25 + -36.75

Combine like terms: -38.25 + -36.75 = -75
x = -75

Simplifying
x = -75


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, -75}

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