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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -14x + -6x = -20x
-6 + -20x + 2x2 = 6 + 6x + -6 + -6x

Reorder the terms:
-6 + -20x + 2x2 = 6 + -6 + 6x + -6x

Combine like terms: 6 + -6 = 0
-6 + -20x + 2x2 = 0 + 6x + -6x
-6 + -20x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6 + -20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -10x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + -10x + x2 = 0

Solving
-3 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -10x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -10x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -10x + x2 = 0 + 3
-10x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-10x + x2 = 3

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 3 + 25

Reorder the terms:
25 + -10x + x2 = 3 + 25

Combine like terms: 3 + 25 = 28
25 + -10x + x2 = 28

Factor a perfect square on the left side:
(x + -5)(x + -5) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -5) equal to 5.291502622 and -5.291502622.

Subproblem 1
x + -5 = 5.291502622

Simplifying
x + -5 = 5.291502622

Reorder the terms:
-5 + x = 5.291502622

Solving
-5 + x = 5.291502622

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.291502622 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.291502622 + 5
x = 5.291502622 + 5

Combine like terms: 5.291502622 + 5 = 10.291502622
x = 10.291502622

Simplifying
x = 10.291502622

Subproblem 2
x + -5 = -5.291502622

Simplifying
x + -5 = -5.291502622

Reorder the terms:
-5 + x = -5.291502622

Solving
-5 + x = -5.291502622

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.291502622 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.291502622 + 5
x = -5.291502622 + 5

Combine like terms: -5.291502622 + 5 = -0.291502622
x = -0.291502622

Simplifying
x = -0.291502622

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.291502622, -0.291502622}
Solution
x = {10.291502622, -0.291502622}