6(1-8x)=10x(10-6x)

Solution for 6(1-8x)=10x(10-6x) equation:

Simplifying
6(1 + -8x) = 10x(10 + -6x)
(1 * 6 + -8x * 6) = 10x(10 + -6x)
(6 + -48x) = 10x(10 + -6x)
6 + -48x = (10 * 10x + -6x * 10x)
6 + -48x = (100x + -60x2)

Solving
6 + -48x = 100x + -60x2

Solving for variable 'x'.

Combine like terms: -48x + -100x = -148x
6 + -148x + 60x2 = 100x + -60x2 + -100x + 60x2

Reorder the terms:
6 + -148x + 60x2 = 100x + -100x + -60x2 + 60x2

Combine like terms: 100x + -100x = 0
6 + -148x + 60x2 = 0 + -60x2 + 60x2
6 + -148x + 60x2 = -60x2 + 60x2

Combine like terms: -60x2 + 60x2 = 0
6 + -148x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -74x + 30x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -74x + 30x2)' equal to zero and attempt to solve:

Simplifying
3 + -74x + 30x2 = 0

Solving
3 + -74x + 30x2 = 0

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

Divide each side by '30'.
0.1 + -2.466666667x + x2 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -2.466666667x + -0.1 + x2 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + -2.466666667x + x2 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -2.466666667x + x2 = 0.0 + -0.1
-2.466666667x + x2 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
-2.466666667x + x2 = -0.1

The x term is -2.466666667x.  Take half its coefficient (-1.233333334).
Square it (1.521111113) and add it to both sides.

Add '1.521111113' to each side of the equation.
-2.466666667x + 1.521111113 + x2 = -0.1 + 1.521111113

Reorder the terms:
1.521111113 + -2.466666667x + x2 = -0.1 + 1.521111113

Combine like terms: -0.1 + 1.521111113 = 1.421111113
1.521111113 + -2.466666667x + x2 = 1.421111113

Factor a perfect square on the left side:
(x + -1.233333334)(x + -1.233333334) = 1.421111113

Calculate the square root of the right side: 1.19210365

Break this problem into two subproblems by setting 
(x + -1.233333334) equal to 1.19210365 and -1.19210365.

Subproblem 1
x + -1.233333334 = 1.19210365

Simplifying
x + -1.233333334 = 1.19210365

Reorder the terms:
-1.233333334 + x = 1.19210365

Solving
-1.233333334 + x = 1.19210365

Solving for variable 'x'.

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

Add '1.233333334' to each side of the equation.
-1.233333334 + 1.233333334 + x = 1.19210365 + 1.233333334

Combine like terms: -1.233333334 + 1.233333334 = 0.000000000
0.000000000 + x = 1.19210365 + 1.233333334
x = 1.19210365 + 1.233333334

Combine like terms: 1.19210365 + 1.233333334 = 2.425436984
x = 2.425436984

Simplifying
x = 2.425436984

Subproblem 2
x + -1.233333334 = -1.19210365

Simplifying
x + -1.233333334 = -1.19210365

Reorder the terms:
-1.233333334 + x = -1.19210365

Solving
-1.233333334 + x = -1.19210365

Solving for variable 'x'.

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

Add '1.233333334' to each side of the equation.
-1.233333334 + 1.233333334 + x = -1.19210365 + 1.233333334

Combine like terms: -1.233333334 + 1.233333334 = 0.000000000
0.000000000 + x = -1.19210365 + 1.233333334
x = -1.19210365 + 1.233333334

Combine like terms: -1.19210365 + 1.233333334 = 0.041229684
x = 0.041229684

Simplifying
x = 0.041229684

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.425436984, 0.041229684}
Solution
x = {2.425436984, 0.041229684}