(1-3x)(2.5x+6)=0

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Solution for (1-3x)(2.5x+6)=0 equation: 


Simplifying
(1 + -3x)(2.5x + 6) = 0

Reorder the terms:
(1 + -3x)(6 + 2.5x) = 0

Multiply (1 + -3x) * (6 + 2.5x)
(1(6 + 2.5x) + -3x * (6 + 2.5x)) = 0
((6 * 1 + 2.5x * 1) + -3x * (6 + 2.5x)) = 0
((6 + 2.5x) + -3x * (6 + 2.5x)) = 0
(6 + 2.5x + (6 * -3x + 2.5x * -3x)) = 0
(6 + 2.5x + (-18x + -7.5x2)) = 0

Combine like terms: 2.5x + -18x = -15.5x
(6 + -15.5x + -7.5x2) = 0

Solving
6 + -15.5x + -7.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7.5 the coefficient of the squared term: 

Divide each side by '-7.5'.
-0.8 + 2.066666667x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 2.066666667x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 2.066666667x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 2.066666667x + x2 = 0 + 0.8
2.066666667x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
2.066666667x + x2 = 0.8

The x term is 2.066666667x.  Take half its coefficient (1.033333334).
Square it (1.067777779) and add it to both sides.

Add '1.067777779' to each side of the equation.
2.066666667x + 1.067777779 + x2 = 0.8 + 1.067777779

Reorder the terms:
1.067777779 + 2.066666667x + x2 = 0.8 + 1.067777779

Combine like terms: 0.8 + 1.067777779 = 1.867777779
1.067777779 + 2.066666667x + x2 = 1.867777779

Factor a perfect square on the left side:
(x + 1.033333334)(x + 1.033333334) = 1.867777779

Calculate the square root of the right side: 1.366666667

Break this problem into two subproblems by setting 
(x + 1.033333334) equal to 1.366666667 and -1.366666667.


Subproblem 1
x + 1.033333334 = 1.366666667

Simplifying
x + 1.033333334 = 1.366666667

Reorder the terms:
1.033333334 + x = 1.366666667

Solving
1.033333334 + x = 1.366666667

Solving for variable 'x'.

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

Add '-1.033333334' to each side of the equation.
1.033333334 + -1.033333334 + x = 1.366666667 + -1.033333334

Combine like terms: 1.033333334 + -1.033333334 = 0.000000000
0.000000000 + x = 1.366666667 + -1.033333334
x = 1.366666667 + -1.033333334

Combine like terms: 1.366666667 + -1.033333334 = 0.333333333
x = 0.333333333

Simplifying
x = 0.333333333


Subproblem 2
x + 1.033333334 = -1.366666667

Simplifying
x + 1.033333334 = -1.366666667

Reorder the terms:
1.033333334 + x = -1.366666667

Solving
1.033333334 + x = -1.366666667

Solving for variable 'x'.

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

Add '-1.033333334' to each side of the equation.
1.033333334 + -1.033333334 + x = -1.366666667 + -1.033333334

Combine like terms: 1.033333334 + -1.033333334 = 0.000000000
0.000000000 + x = -1.366666667 + -1.033333334
x = -1.366666667 + -1.033333334

Combine like terms: -1.366666667 + -1.033333334 = -2.400000001
x = -2.400000001

Simplifying
x = -2.400000001


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.333333333, -2.400000001}

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