(2x+0.67)(0.25-2x)=0

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Solution for (2x+0.67)(0.25-2x)=0 equation: 


Simplifying
(2x + 0.67)(0.25 + -2x) = 0

Reorder the terms:
(0.67 + 2x)(0.25 + -2x) = 0

Multiply (0.67 + 2x) * (0.25 + -2x)
(0.67(0.25 + -2x) + 2x * (0.25 + -2x)) = 0
((0.25 * 0.67 + -2x * 0.67) + 2x * (0.25 + -2x)) = 0
((0.1675 + -1.34x) + 2x * (0.25 + -2x)) = 0
(0.1675 + -1.34x + (0.25 * 2x + -2x * 2x)) = 0
(0.1675 + -1.34x + (0.5x + -4x2)) = 0

Combine like terms: -1.34x + 0.5x = -0.84x
(0.1675 + -0.84x + -4x2) = 0

Solving
0.1675 + -0.84x + -4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.041875 + 0.21x + x2 = 0

Move the constant term to the right:

Add '0.041875' to each side of the equation.
-0.041875 + 0.21x + 0.041875 + x2 = 0 + 0.041875

Reorder the terms:
-0.041875 + 0.041875 + 0.21x + x2 = 0 + 0.041875

Combine like terms: -0.041875 + 0.041875 = 0.000000
0.000000 + 0.21x + x2 = 0 + 0.041875
0.21x + x2 = 0 + 0.041875

Combine like terms: 0 + 0.041875 = 0.041875
0.21x + x2 = 0.041875

The x term is 0.21x.  Take half its coefficient (0.105).
Square it (0.011025) and add it to both sides.

Add '0.011025' to each side of the equation.
0.21x + 0.011025 + x2 = 0.041875 + 0.011025

Reorder the terms:
0.011025 + 0.21x + x2 = 0.041875 + 0.011025

Combine like terms: 0.041875 + 0.011025 = 0.0529
0.011025 + 0.21x + x2 = 0.0529

Factor a perfect square on the left side:
(x + 0.105)(x + 0.105) = 0.0529

Calculate the square root of the right side: 0.23

Break this problem into two subproblems by setting 
(x + 0.105) equal to 0.23 and -0.23.


Subproblem 1
x + 0.105 = 0.23

Simplifying
x + 0.105 = 0.23

Reorder the terms:
0.105 + x = 0.23

Solving
0.105 + x = 0.23

Solving for variable 'x'.

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

Add '-0.105' to each side of the equation.
0.105 + -0.105 + x = 0.23 + -0.105

Combine like terms: 0.105 + -0.105 = 0.000
0.000 + x = 0.23 + -0.105
x = 0.23 + -0.105

Combine like terms: 0.23 + -0.105 = 0.125
x = 0.125

Simplifying
x = 0.125


Subproblem 2
x + 0.105 = -0.23

Simplifying
x + 0.105 = -0.23

Reorder the terms:
0.105 + x = -0.23

Solving
0.105 + x = -0.23

Solving for variable 'x'.

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

Add '-0.105' to each side of the equation.
0.105 + -0.105 + x = -0.23 + -0.105

Combine like terms: 0.105 + -0.105 = 0.000
0.000 + x = -0.23 + -0.105
x = -0.23 + -0.105

Combine like terms: -0.23 + -0.105 = -0.335
x = -0.335

Simplifying
x = -0.335


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.125, -0.335}

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