28(2x-1)=7(x+3)22x

Solution for 28(2x-1)=7(x+3)22x equation:

Simplifying
28(2x + -1) = 7(x + 3) * 22x

Reorder the terms:
28(-1 + 2x) = 7(x + 3) * 22x
(-1 * 28 + 2x * 28) = 7(x + 3) * 22x
(-28 + 56x) = 7(x + 3) * 22x

Reorder the terms:
-28 + 56x = 7(3 + x) * 22x

Reorder the terms for easier multiplication:
-28 + 56x = 7 * 22x(3 + x)

Multiply 7 * 22
-28 + 56x = 154x(3 + x)
-28 + 56x = (3 * 154x + x * 154x)
-28 + 56x = (462x + 154x2)

Solving
-28 + 56x = 462x + 154x2

Solving for variable 'x'.

Combine like terms: 56x + -462x = -406x
-28 + -406x + -154x2 = 462x + 154x2 + -462x + -154x2

Reorder the terms:
-28 + -406x + -154x2 = 462x + -462x + 154x2 + -154x2

Combine like terms: 462x + -462x = 0
-28 + -406x + -154x2 = 0 + 154x2 + -154x2
-28 + -406x + -154x2 = 154x2 + -154x2

Combine like terms: 154x2 + -154x2 = 0
-28 + -406x + -154x2 = 0

Factor out the Greatest Common Factor (GCF), '-14'.
-14(2 + 29x + 11x2) = 0

Ignore the factor -14.
Subproblem 1
Set the factor '(2 + 29x + 11x2)' equal to zero and attempt to solve:

Simplifying
2 + 29x + 11x2 = 0

Solving
2 + 29x + 11x2 = 0

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

Divide each side by '11'.
0.1818181818 + 2.636363636x + x2 = 0

Move the constant term to the right:

Add '-0.1818181818' to each side of the equation.
0.1818181818 + 2.636363636x + -0.1818181818 + x2 = 0 + -0.1818181818

Reorder the terms:
0.1818181818 + -0.1818181818 + 2.636363636x + x2 = 0 + -0.1818181818

Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000
0.0000000000 + 2.636363636x + x2 = 0 + -0.1818181818
2.636363636x + x2 = 0 + -0.1818181818

Combine like terms: 0 + -0.1818181818 = -0.1818181818
2.636363636x + x2 = -0.1818181818

The x term is 2.636363636x.  Take half its coefficient (1.318181818).
Square it (1.737603305) and add it to both sides.

Add '1.737603305' to each side of the equation.
2.636363636x + 1.737603305 + x2 = -0.1818181818 + 1.737603305

Reorder the terms:
1.737603305 + 2.636363636x + x2 = -0.1818181818 + 1.737603305

Combine like terms: -0.1818181818 + 1.737603305 = 1.5557851232
1.737603305 + 2.636363636x + x2 = 1.5557851232

Factor a perfect square on the left side:
(x + 1.318181818)(x + 1.318181818) = 1.5557851232

Calculate the square root of the right side: 1.247311157

Break this problem into two subproblems by setting 
(x + 1.318181818) equal to 1.247311157 and -1.247311157.

Subproblem 1
x + 1.318181818 = 1.247311157

Simplifying
x + 1.318181818 = 1.247311157

Reorder the terms:
1.318181818 + x = 1.247311157

Solving
1.318181818 + x = 1.247311157

Solving for variable 'x'.

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

Add '-1.318181818' to each side of the equation.
1.318181818 + -1.318181818 + x = 1.247311157 + -1.318181818

Combine like terms: 1.318181818 + -1.318181818 = 0.000000000
0.000000000 + x = 1.247311157 + -1.318181818
x = 1.247311157 + -1.318181818

Combine like terms: 1.247311157 + -1.318181818 = -0.070870661
x = -0.070870661

Simplifying
x = -0.070870661

Subproblem 2
x + 1.318181818 = -1.247311157

Simplifying
x + 1.318181818 = -1.247311157

Reorder the terms:
1.318181818 + x = -1.247311157

Solving
1.318181818 + x = -1.247311157

Solving for variable 'x'.

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

Add '-1.318181818' to each side of the equation.
1.318181818 + -1.318181818 + x = -1.247311157 + -1.318181818

Combine like terms: 1.318181818 + -1.318181818 = 0.000000000
0.000000000 + x = -1.247311157 + -1.318181818
x = -1.247311157 + -1.318181818

Combine like terms: -1.247311157 + -1.318181818 = -2.565492975
x = -2.565492975

Simplifying
x = -2.565492975

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.070870661, -2.565492975}
Solution
x = {-0.070870661, -2.565492975}