6(6x-1)+5(6-3x)4(5x+1)=2

Solution for 6(6x-1)+5(6-3x)4(5x+1)=2 equation:

Simplifying
6(6x + -1) + 5(6 + -3x) * 4(5x + 1) = 2

Reorder the terms:
6(-1 + 6x) + 5(6 + -3x) * 4(5x + 1) = 2
(-1 * 6 + 6x * 6) + 5(6 + -3x) * 4(5x + 1) = 2
(-6 + 36x) + 5(6 + -3x) * 4(5x + 1) = 2

Reorder the terms:
-6 + 36x + 5(6 + -3x) * 4(1 + 5x) = 2

Reorder the terms for easier multiplication:
-6 + 36x + 5 * 4(6 + -3x)(1 + 5x) = 2

Multiply 5 * 4
-6 + 36x + 20(6 + -3x)(1 + 5x) = 2

Multiply (6 + -3x) * (1 + 5x)
-6 + 36x + 20(6(1 + 5x) + -3x * (1 + 5x)) = 2
-6 + 36x + 20((1 * 6 + 5x * 6) + -3x * (1 + 5x)) = 2
-6 + 36x + 20((6 + 30x) + -3x * (1 + 5x)) = 2
-6 + 36x + 20(6 + 30x + (1 * -3x + 5x * -3x)) = 2
-6 + 36x + 20(6 + 30x + (-3x + -15x2)) = 2

Combine like terms: 30x + -3x = 27x
-6 + 36x + 20(6 + 27x + -15x2) = 2
-6 + 36x + (6 * 20 + 27x * 20 + -15x2 * 20) = 2
-6 + 36x + (120 + 540x + -300x2) = 2

Reorder the terms:
-6 + 120 + 36x + 540x + -300x2 = 2

Combine like terms: -6 + 120 = 114
114 + 36x + 540x + -300x2 = 2

Combine like terms: 36x + 540x = 576x
114 + 576x + -300x2 = 2

Solving
114 + 576x + -300x2 = 2

Solving for variable 'x'.

Reorder the terms:
114 + -2 + 576x + -300x2 = 2 + -2

Combine like terms: 114 + -2 = 112
112 + 576x + -300x2 = 2 + -2

Combine like terms: 2 + -2 = 0
112 + 576x + -300x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(28 + 144x + -75x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(28 + 144x + -75x2)' equal to zero and attempt to solve:

Simplifying
28 + 144x + -75x2 = 0

Solving
28 + 144x + -75x2 = 0

Begin completing the square.  Divide all terms by
-75 the coefficient of the squared term: 

Divide each side by '-75'.
-0.3733333333 + -1.92x + x2 = 0

Move the constant term to the right:

Add '0.3733333333' to each side of the equation.
-0.3733333333 + -1.92x + 0.3733333333 + x2 = 0 + 0.3733333333

Reorder the terms:
-0.3733333333 + 0.3733333333 + -1.92x + x2 = 0 + 0.3733333333

Combine like terms: -0.3733333333 + 0.3733333333 = 0.0000000000
0.0000000000 + -1.92x + x2 = 0 + 0.3733333333
-1.92x + x2 = 0 + 0.3733333333

Combine like terms: 0 + 0.3733333333 = 0.3733333333
-1.92x + x2 = 0.3733333333

The x term is -1.92x.  Take half its coefficient (-0.96).
Square it (0.9216) and add it to both sides.

Add '0.9216' to each side of the equation.
-1.92x + 0.9216 + x2 = 0.3733333333 + 0.9216

Reorder the terms:
0.9216 + -1.92x + x2 = 0.3733333333 + 0.9216

Combine like terms: 0.3733333333 + 0.9216 = 1.2949333333
0.9216 + -1.92x + x2 = 1.2949333333

Factor a perfect square on the left side:
(x + -0.96)(x + -0.96) = 1.2949333333

Calculate the square root of the right side: 1.137951376

Break this problem into two subproblems by setting 
(x + -0.96) equal to 1.137951376 and -1.137951376.

Subproblem 1
x + -0.96 = 1.137951376

Simplifying
x + -0.96 = 1.137951376

Reorder the terms:
-0.96 + x = 1.137951376

Solving
-0.96 + x = 1.137951376

Solving for variable 'x'.

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

Add '0.96' to each side of the equation.
-0.96 + 0.96 + x = 1.137951376 + 0.96

Combine like terms: -0.96 + 0.96 = 0.00
0.00 + x = 1.137951376 + 0.96
x = 1.137951376 + 0.96

Combine like terms: 1.137951376 + 0.96 = 2.097951376
x = 2.097951376

Simplifying
x = 2.097951376

Subproblem 2
x + -0.96 = -1.137951376

Simplifying
x + -0.96 = -1.137951376

Reorder the terms:
-0.96 + x = -1.137951376

Solving
-0.96 + x = -1.137951376

Solving for variable 'x'.

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

Add '0.96' to each side of the equation.
-0.96 + 0.96 + x = -1.137951376 + 0.96

Combine like terms: -0.96 + 0.96 = 0.00
0.00 + x = -1.137951376 + 0.96
x = -1.137951376 + 0.96

Combine like terms: -1.137951376 + 0.96 = -0.177951376
x = -0.177951376

Simplifying
x = -0.177951376

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.097951376, -0.177951376}
Solution
x = {2.097951376, -0.177951376}