-2x(x-7)+6=1(x-5)

Solution for -2x(x-7)+6=1(x-5) equation:

Simplifying
-2x(x + -7) + 6 = 1(x + -5)

Reorder the terms:
-2x(-7 + x) + 6 = 1(x + -5)
(-7 * -2x + x * -2x) + 6 = 1(x + -5)
(14x + -2x2) + 6 = 1(x + -5)

Reorder the terms:
6 + 14x + -2x2 = 1(x + -5)

Reorder the terms:
6 + 14x + -2x2 = 1(-5 + x)
6 + 14x + -2x2 = (-5 * 1 + x * 1)
6 + 14x + -2x2 = (-5 + 1x)

Solving
6 + 14x + -2x2 = -5 + 1x

Solving for variable 'x'.

Reorder the terms:
6 + 5 + 14x + -1x + -2x2 = -5 + 1x + 5 + -1x

Combine like terms: 6 + 5 = 11
11 + 14x + -1x + -2x2 = -5 + 1x + 5 + -1x

Combine like terms: 14x + -1x = 13x
11 + 13x + -2x2 = -5 + 1x + 5 + -1x

Reorder the terms:
11 + 13x + -2x2 = -5 + 5 + 1x + -1x

Combine like terms: -5 + 5 = 0
11 + 13x + -2x2 = 0 + 1x + -1x
11 + 13x + -2x2 = 1x + -1x

Combine like terms: 1x + -1x = 0
11 + 13x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-5.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -6.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -6.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -6.5x + x2 = 0 + 5.5
-6.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-6.5x + x2 = 5.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 5.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 5.5 + 10.5625

Combine like terms: 5.5 + 10.5625 = 16.0625
10.5625 + -6.5x + x2 = 16.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 16.0625

Calculate the square root of the right side: 4.007804885

Break this problem into two subproblems by setting 
(x + -3.25) equal to 4.007804885 and -4.007804885.

Subproblem 1
x + -3.25 = 4.007804885

Simplifying
x + -3.25 = 4.007804885

Reorder the terms:
-3.25 + x = 4.007804885

Solving
-3.25 + x = 4.007804885

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 4.007804885 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 4.007804885 + 3.25
x = 4.007804885 + 3.25

Combine like terms: 4.007804885 + 3.25 = 7.257804885
x = 7.257804885

Simplifying
x = 7.257804885

Subproblem 2
x + -3.25 = -4.007804885

Simplifying
x + -3.25 = -4.007804885

Reorder the terms:
-3.25 + x = -4.007804885

Solving
-3.25 + x = -4.007804885

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -4.007804885 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -4.007804885 + 3.25
x = -4.007804885 + 3.25

Combine like terms: -4.007804885 + 3.25 = -0.757804885
x = -0.757804885

Simplifying
x = -0.757804885

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.257804885, -0.757804885}