14(x-1)=-7(2-x)7x

Solution for 14(x-1)=-7(2-x)7x equation:

Simplifying
14(x + -1) = -7(2 + -1x) * 7x

Reorder the terms:
14(-1 + x) = -7(2 + -1x) * 7x
(-1 * 14 + x * 14) = -7(2 + -1x) * 7x
(-14 + 14x) = -7(2 + -1x) * 7x

Reorder the terms for easier multiplication:
-14 + 14x = -7 * 7x(2 + -1x)

Multiply -7 * 7
-14 + 14x = -49x(2 + -1x)
-14 + 14x = (2 * -49x + -1x * -49x)
-14 + 14x = (-98x + 49x2)

Solving
-14 + 14x = -98x + 49x2

Solving for variable 'x'.

Combine like terms: 14x + 98x = 112x
-14 + 112x + -49x2 = -98x + 49x2 + 98x + -49x2

Reorder the terms:
-14 + 112x + -49x2 = -98x + 98x + 49x2 + -49x2

Combine like terms: -98x + 98x = 0
-14 + 112x + -49x2 = 0 + 49x2 + -49x2
-14 + 112x + -49x2 = 49x2 + -49x2

Combine like terms: 49x2 + -49x2 = 0
-14 + 112x + -49x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-2 + 16x + -7x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-2 + 16x + -7x2)' equal to zero and attempt to solve:

Simplifying
-2 + 16x + -7x2 = 0

Solving
-2 + 16x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.2857142857 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -2.285714286x + -0.2857142857 + x2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -2.285714286x + x2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -2.285714286x + x2 = 0 + -0.2857142857
-2.285714286x + x2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-2.285714286x + x2 = -0.2857142857

The x term is -2.285714286x.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286x + 1.306122449 + x2 = -0.2857142857 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = -0.2857142857 + 1.306122449

Combine like terms: -0.2857142857 + 1.306122449 = 1.0204081633
1.306122449 + -2.285714286x + x2 = 1.0204081633

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 1.0204081633

Calculate the square root of the right side: 1.010152545

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 1.010152545 and -1.010152545.

Subproblem 1
x + -1.142857143 = 1.010152545

Simplifying
x + -1.142857143 = 1.010152545

Reorder the terms:
-1.142857143 + x = 1.010152545

Solving
-1.142857143 + x = 1.010152545

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = 1.010152545 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = 1.010152545 + 1.142857143
x = 1.010152545 + 1.142857143

Combine like terms: 1.010152545 + 1.142857143 = 2.153009688
x = 2.153009688

Simplifying
x = 2.153009688

Subproblem 2
x + -1.142857143 = -1.010152545

Simplifying
x + -1.142857143 = -1.010152545

Reorder the terms:
-1.142857143 + x = -1.010152545

Solving
-1.142857143 + x = -1.010152545

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = -1.010152545 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = -1.010152545 + 1.142857143
x = -1.010152545 + 1.142857143

Combine like terms: -1.010152545 + 1.142857143 = 0.132704598
x = 0.132704598

Simplifying
x = 0.132704598

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.153009688, 0.132704598}
Solution
x = {2.153009688, 0.132704598}