6(1+3x)=2(10x-9)4x

Solution for 6(1+3x)=2(10x-9)4x equation:

Simplifying
6(1 + 3x) = 2(10x + -9) * 4x
(1 * 6 + 3x * 6) = 2(10x + -9) * 4x
(6 + 18x) = 2(10x + -9) * 4x

Reorder the terms:
6 + 18x = 2(-9 + 10x) * 4x

Reorder the terms for easier multiplication:
6 + 18x = 2 * 4x(-9 + 10x)

Multiply 2 * 4
6 + 18x = 8x(-9 + 10x)
6 + 18x = (-9 * 8x + 10x * 8x)
6 + 18x = (-72x + 80x2)

Solving
6 + 18x = -72x + 80x2

Solving for variable 'x'.

Combine like terms: 18x + 72x = 90x
6 + 90x + -80x2 = -72x + 80x2 + 72x + -80x2

Reorder the terms:
6 + 90x + -80x2 = -72x + 72x + 80x2 + -80x2

Combine like terms: -72x + 72x = 0
6 + 90x + -80x2 = 0 + 80x2 + -80x2
6 + 90x + -80x2 = 80x2 + -80x2

Combine like terms: 80x2 + -80x2 = 0
6 + 90x + -80x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 45x + -40x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 45x + -40x2)' equal to zero and attempt to solve:

Simplifying
3 + 45x + -40x2 = 0

Solving
3 + 45x + -40x2 = 0

Begin completing the square.  Divide all terms by
-40 the coefficient of the squared term: 

Divide each side by '-40'.
-0.075 + -1.125x + x2 = 0.0

Move the constant term to the right:

Add '0.075' to each side of the equation.
-0.075 + -1.125x + 0.075 + x2 = 0.0 + 0.075

Reorder the terms:
-0.075 + 0.075 + -1.125x + x2 = 0.0 + 0.075

Combine like terms: -0.075 + 0.075 = 0.000
0.000 + -1.125x + x2 = 0.0 + 0.075
-1.125x + x2 = 0.0 + 0.075

Combine like terms: 0.0 + 0.075 = 0.075
-1.125x + x2 = 0.075

The x term is -1.125x.  Take half its coefficient (-0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
-1.125x + 0.31640625 + x2 = 0.075 + 0.31640625

Reorder the terms:
0.31640625 + -1.125x + x2 = 0.075 + 0.31640625

Combine like terms: 0.075 + 0.31640625 = 0.39140625
0.31640625 + -1.125x + x2 = 0.39140625

Factor a perfect square on the left side:
(x + -0.5625)(x + -0.5625) = 0.39140625

Calculate the square root of the right side: 0.625624688

Break this problem into two subproblems by setting 
(x + -0.5625) equal to 0.625624688 and -0.625624688.

Subproblem 1
x + -0.5625 = 0.625624688

Simplifying
x + -0.5625 = 0.625624688

Reorder the terms:
-0.5625 + x = 0.625624688

Solving
-0.5625 + x = 0.625624688

Solving for variable 'x'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + x = 0.625624688 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + x = 0.625624688 + 0.5625
x = 0.625624688 + 0.5625

Combine like terms: 0.625624688 + 0.5625 = 1.188124688
x = 1.188124688

Simplifying
x = 1.188124688

Subproblem 2
x + -0.5625 = -0.625624688

Simplifying
x + -0.5625 = -0.625624688

Reorder the terms:
-0.5625 + x = -0.625624688

Solving
-0.5625 + x = -0.625624688

Solving for variable 'x'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + x = -0.625624688 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + x = -0.625624688 + 0.5625
x = -0.625624688 + 0.5625

Combine like terms: -0.625624688 + 0.5625 = -0.063124688
x = -0.063124688

Simplifying
x = -0.063124688

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.188124688, -0.063124688}
Solution
x = {1.188124688, -0.063124688}