4(2x-1)35(2x-1)=8

Solution for 4(2x-1)35(2x-1)=8 equation:

Simplifying
4(2x + -1) * 35(2x + -1) = 8

Reorder the terms:
4(-1 + 2x) * 35(2x + -1) = 8

Reorder the terms:
4(-1 + 2x) * 35(-1 + 2x) = 8

Reorder the terms for easier multiplication:
4 * 35(-1 + 2x)(-1 + 2x) = 8

Multiply 4 * 35
140(-1 + 2x)(-1 + 2x) = 8

Multiply (-1 + 2x) * (-1 + 2x)
140(-1(-1 + 2x) + 2x * (-1 + 2x)) = 8
140((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 8
140((1 + -2x) + 2x * (-1 + 2x)) = 8
140(1 + -2x + (-1 * 2x + 2x * 2x)) = 8
140(1 + -2x + (-2x + 4x2)) = 8

Combine like terms: -2x + -2x = -4x
140(1 + -4x + 4x2) = 8
(1 * 140 + -4x * 140 + 4x2 * 140) = 8
(140 + -560x + 560x2) = 8

Solving
140 + -560x + 560x2 = 8

Solving for variable 'x'.

Reorder the terms:
140 + -8 + -560x + 560x2 = 8 + -8

Combine like terms: 140 + -8 = 132
132 + -560x + 560x2 = 8 + -8

Combine like terms: 8 + -8 = 0
132 + -560x + 560x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(33 + -140x + 140x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(33 + -140x + 140x2)' equal to zero and attempt to solve:

Simplifying
33 + -140x + 140x2 = 0

Solving
33 + -140x + 140x2 = 0

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

Divide each side by '140'.
0.2357142857 + -1x + x2 = 0.0

Move the constant term to the right:

Add '-0.2357142857' to each side of the equation.
0.2357142857 + -1x + -0.2357142857 + x2 = 0.0 + -0.2357142857

Reorder the terms:
0.2357142857 + -0.2357142857 + -1x + x2 = 0.0 + -0.2357142857

Combine like terms: 0.2357142857 + -0.2357142857 = 0.0000000000
0.0000000000 + -1x + x2 = 0.0 + -0.2357142857
-1x + x2 = 0.0 + -0.2357142857

Combine like terms: 0.0 + -0.2357142857 = -0.2357142857
-1x + x2 = -0.2357142857

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.2357142857 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.2357142857 + 0.25

Combine like terms: -0.2357142857 + 0.25 = 0.0142857143
0.25 + -1x + x2 = 0.0142857143

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.0142857143

Calculate the square root of the right side: 0.119522861

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.119522861 and -0.119522861.

Subproblem 1
x + -0.5 = 0.119522861

Simplifying
x + -0.5 = 0.119522861

Reorder the terms:
-0.5 + x = 0.119522861

Solving
-0.5 + x = 0.119522861

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.119522861 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.119522861 + 0.5
x = 0.119522861 + 0.5

Combine like terms: 0.119522861 + 0.5 = 0.619522861
x = 0.619522861

Simplifying
x = 0.619522861

Subproblem 2
x + -0.5 = -0.119522861

Simplifying
x + -0.5 = -0.119522861

Reorder the terms:
-0.5 + x = -0.119522861

Solving
-0.5 + x = -0.119522861

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.119522861 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.119522861 + 0.5
x = -0.119522861 + 0.5

Combine like terms: -0.119522861 + 0.5 = 0.380477139
x = 0.380477139

Simplifying
x = 0.380477139

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.619522861, 0.380477139}
Solution
x = {0.619522861, 0.380477139}