2x(x-3)-4(7+2x)=2(x-1)

Solution for 2x(x-3)-4(7+2x)=2(x-1) equation:

Simplifying
2x(x + -3) + -4(7 + 2x) = 2(x + -1)

Reorder the terms:
2x(-3 + x) + -4(7 + 2x) = 2(x + -1)
(-3 * 2x + x * 2x) + -4(7 + 2x) = 2(x + -1)
(-6x + 2x2) + -4(7 + 2x) = 2(x + -1)
-6x + 2x2 + (7 * -4 + 2x * -4) = 2(x + -1)
-6x + 2x2 + (-28 + -8x) = 2(x + -1)

Reorder the terms:
-28 + -6x + -8x + 2x2 = 2(x + -1)

Combine like terms: -6x + -8x = -14x
-28 + -14x + 2x2 = 2(x + -1)

Reorder the terms:
-28 + -14x + 2x2 = 2(-1 + x)
-28 + -14x + 2x2 = (-1 * 2 + x * 2)
-28 + -14x + 2x2 = (-2 + 2x)

Solving
-28 + -14x + 2x2 = -2 + 2x

Solving for variable 'x'.

Reorder the terms:
-28 + 2 + -14x + -2x + 2x2 = -2 + 2x + 2 + -2x

Combine like terms: -28 + 2 = -26
-26 + -14x + -2x + 2x2 = -2 + 2x + 2 + -2x

Combine like terms: -14x + -2x = -16x
-26 + -16x + 2x2 = -2 + 2x + 2 + -2x

Reorder the terms:
-26 + -16x + 2x2 = -2 + 2 + 2x + -2x

Combine like terms: -2 + 2 = 0
-26 + -16x + 2x2 = 0 + 2x + -2x
-26 + -16x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-26 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + -8x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-13 + -8x + x2 = 0

Solving
-13 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -8x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -8x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -8x + x2 = 0 + 13
-8x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-8x + x2 = 13

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 13 + 16

Reorder the terms:
16 + -8x + x2 = 13 + 16

Combine like terms: 13 + 16 = 29
16 + -8x + x2 = 29

Factor a perfect square on the left side:
(x + -4)(x + -4) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + -4) equal to 5.385164807 and -5.385164807.

Subproblem 1
x + -4 = 5.385164807

Simplifying
x + -4 = 5.385164807

Reorder the terms:
-4 + x = 5.385164807

Solving
-4 + x = 5.385164807

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 5.385164807 + 4

Combine like terms: -4 + 4 = 0
0 + x = 5.385164807 + 4
x = 5.385164807 + 4

Combine like terms: 5.385164807 + 4 = 9.385164807
x = 9.385164807

Simplifying
x = 9.385164807

Subproblem 2
x + -4 = -5.385164807

Simplifying
x + -4 = -5.385164807

Reorder the terms:
-4 + x = -5.385164807

Solving
-4 + x = -5.385164807

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -5.385164807 + 4

Combine like terms: -4 + 4 = 0
0 + x = -5.385164807 + 4
x = -5.385164807 + 4

Combine like terms: -5.385164807 + 4 = -1.385164807
x = -1.385164807

Simplifying
x = -1.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.385164807, -1.385164807}
Solution
x = {9.385164807, -1.385164807}