(x+2)(12x-5)=12-5x

Solution for (x+2)(12x-5)=12-5x equation:

Simplifying
(x + 2)(12x + -5) = 12 + -5x

Reorder the terms:
(2 + x)(12x + -5) = 12 + -5x

Reorder the terms:
(2 + x)(-5 + 12x) = 12 + -5x

Multiply (2 + x) * (-5 + 12x)
(2(-5 + 12x) + x(-5 + 12x)) = 12 + -5x
((-5 * 2 + 12x * 2) + x(-5 + 12x)) = 12 + -5x
((-10 + 24x) + x(-5 + 12x)) = 12 + -5x
(-10 + 24x + (-5 * x + 12x * x)) = 12 + -5x
(-10 + 24x + (-5x + 12x2)) = 12 + -5x

Combine like terms: 24x + -5x = 19x
(-10 + 19x + 12x2) = 12 + -5x

Solving
-10 + 19x + 12x2 = 12 + -5x

Solving for variable 'x'.

Reorder the terms:
-10 + -12 + 19x + 5x + 12x2 = 12 + -5x + -12 + 5x

Combine like terms: -10 + -12 = -22
-22 + 19x + 5x + 12x2 = 12 + -5x + -12 + 5x

Combine like terms: 19x + 5x = 24x
-22 + 24x + 12x2 = 12 + -5x + -12 + 5x

Reorder the terms:
-22 + 24x + 12x2 = 12 + -12 + -5x + 5x

Combine like terms: 12 + -12 = 0
-22 + 24x + 12x2 = 0 + -5x + 5x
-22 + 24x + 12x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-22 + 24x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 12x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + 12x + 6x2)' equal to zero and attempt to solve:

Simplifying
-11 + 12x + 6x2 = 0

Solving
-11 + 12x + 6x2 = 0

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

Divide each side by '6'.
-1.833333333 + 2x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + 2x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + 2x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 1.833333333
2x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
2x + x2 = 1.833333333

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 = 1.833333333 + 1

Reorder the terms:
1 + 2x + x2 = 1.833333333 + 1

Combine like terms: 1.833333333 + 1 = 2.833333333
1 + 2x + x2 = 2.833333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.833333333

Calculate the square root of the right side: 1.683250823

Break this problem into two subproblems by setting 
(x + 1) equal to 1.683250823 and -1.683250823.

Subproblem 1
x + 1 = 1.683250823

Simplifying
x + 1 = 1.683250823

Reorder the terms:
1 + x = 1.683250823

Solving
1 + x = 1.683250823

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 = 1.683250823 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.683250823 + -1
x = 1.683250823 + -1

Combine like terms: 1.683250823 + -1 = 0.683250823
x = 0.683250823

Simplifying
x = 0.683250823

Subproblem 2
x + 1 = -1.683250823

Simplifying
x + 1 = -1.683250823

Reorder the terms:
1 + x = -1.683250823

Solving
1 + x = -1.683250823

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 = -1.683250823 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.683250823 + -1
x = -1.683250823 + -1

Combine like terms: -1.683250823 + -1 = -2.683250823
x = -2.683250823

Simplifying
x = -2.683250823

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.683250823, -2.683250823}
Solution
x = {0.683250823, -2.683250823}