3x-2x(x-1)=2x+7x-12

Solution for 3x-2x(x-1)=2x+7x-12 equation:

Simplifying
3x + -2x(x + -1) = 2x + 7x + -12

Reorder the terms:
3x + -2x(-1 + x) = 2x + 7x + -12
3x + (-1 * -2x + x * -2x) = 2x + 7x + -12
3x + (2x + -2x2) = 2x + 7x + -12

Combine like terms: 3x + 2x = 5x
5x + -2x2 = 2x + 7x + -12

Reorder the terms:
5x + -2x2 = -12 + 2x + 7x

Combine like terms: 2x + 7x = 9x
5x + -2x2 = -12 + 9x

Solving
5x + -2x2 = -12 + 9x

Solving for variable 'x'.

Reorder the terms:
12 + 5x + -9x + -2x2 = -12 + 9x + 12 + -9x

Combine like terms: 5x + -9x = -4x
12 + -4x + -2x2 = -12 + 9x + 12 + -9x

Reorder the terms:
12 + -4x + -2x2 = -12 + 12 + 9x + -9x

Combine like terms: -12 + 12 = 0
12 + -4x + -2x2 = 0 + 9x + -9x
12 + -4x + -2x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
12 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -2x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -2x + -1x2 = 0

Solving
6 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 2x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 2x + x2 = 0 + 6

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

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

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 6 + 1

Reorder the terms:
1 + 2x + x2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2x + x2 = 7

Factor a perfect square on the left side:
(x + 1)(x + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
x + 1 = 2.645751311

Simplifying
x + 1 = 2.645751311

Reorder the terms:
1 + x = 2.645751311

Solving
1 + x = 2.645751311

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.645751311 + -1
x = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
x = 1.645751311

Simplifying
x = 1.645751311

Subproblem 2
x + 1 = -2.645751311

Simplifying
x + 1 = -2.645751311

Reorder the terms:
1 + x = -2.645751311

Solving
1 + x = -2.645751311

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.645751311 + -1
x = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
x = -3.645751311

Simplifying
x = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.645751311, -3.645751311}
Solution
x = {1.645751311, -3.645751311}