6(4x+3)-20+2(x+9)=10(x-2)12x

Solution for 6(4x+3)-20+2(x+9)=10(x-2)12x equation:

Simplifying
6(4x + 3) + -20 + 2(x + 9) = 10(x + -2) * 12x

Reorder the terms:
6(3 + 4x) + -20 + 2(x + 9) = 10(x + -2) * 12x
(3 * 6 + 4x * 6) + -20 + 2(x + 9) = 10(x + -2) * 12x
(18 + 24x) + -20 + 2(x + 9) = 10(x + -2) * 12x

Reorder the terms:
18 + 24x + -20 + 2(9 + x) = 10(x + -2) * 12x
18 + 24x + -20 + (9 * 2 + x * 2) = 10(x + -2) * 12x
18 + 24x + -20 + (18 + 2x) = 10(x + -2) * 12x

Reorder the terms:
18 + -20 + 18 + 24x + 2x = 10(x + -2) * 12x

Combine like terms: 18 + -20 = -2
-2 + 18 + 24x + 2x = 10(x + -2) * 12x

Combine like terms: -2 + 18 = 16
16 + 24x + 2x = 10(x + -2) * 12x

Combine like terms: 24x + 2x = 26x
16 + 26x = 10(x + -2) * 12x

Reorder the terms:
16 + 26x = 10(-2 + x) * 12x

Reorder the terms for easier multiplication:
16 + 26x = 10 * 12x(-2 + x)

Multiply 10 * 12
16 + 26x = 120x(-2 + x)
16 + 26x = (-2 * 120x + x * 120x)
16 + 26x = (-240x + 120x2)

Solving
16 + 26x = -240x + 120x2

Solving for variable 'x'.

Combine like terms: 26x + 240x = 266x
16 + 266x + -120x2 = -240x + 120x2 + 240x + -120x2

Reorder the terms:
16 + 266x + -120x2 = -240x + 240x + 120x2 + -120x2

Combine like terms: -240x + 240x = 0
16 + 266x + -120x2 = 0 + 120x2 + -120x2
16 + 266x + -120x2 = 120x2 + -120x2

Combine like terms: 120x2 + -120x2 = 0
16 + 266x + -120x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 133x + -60x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + 133x + -60x2)' equal to zero and attempt to solve:

Simplifying
8 + 133x + -60x2 = 0

Solving
8 + 133x + -60x2 = 0

Begin completing the square.  Divide all terms by
-60 the coefficient of the squared term: 

Divide each side by '-60'.
-0.1333333333 + -2.216666667x + x2 = 0.0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + -2.216666667x + 0.1333333333 + x2 = 0.0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + -2.216666667x + x2 = 0.0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + -2.216666667x + x2 = 0.0 + 0.1333333333
-2.216666667x + x2 = 0.0 + 0.1333333333

Combine like terms: 0.0 + 0.1333333333 = 0.1333333333
-2.216666667x + x2 = 0.1333333333

The x term is -2.216666667x.  Take half its coefficient (-1.108333334).
Square it (1.228402779) and add it to both sides.

Add '1.228402779' to each side of the equation.
-2.216666667x + 1.228402779 + x2 = 0.1333333333 + 1.228402779

Reorder the terms:
1.228402779 + -2.216666667x + x2 = 0.1333333333 + 1.228402779

Combine like terms: 0.1333333333 + 1.228402779 = 1.3617361123
1.228402779 + -2.216666667x + x2 = 1.3617361123

Factor a perfect square on the left side:
(x + -1.108333334)(x + -1.108333334) = 1.3617361123

Calculate the square root of the right side: 1.166934494

Break this problem into two subproblems by setting 
(x + -1.108333334) equal to 1.166934494 and -1.166934494.

Subproblem 1
x + -1.108333334 = 1.166934494

Simplifying
x + -1.108333334 = 1.166934494

Reorder the terms:
-1.108333334 + x = 1.166934494

Solving
-1.108333334 + x = 1.166934494

Solving for variable 'x'.

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

Add '1.108333334' to each side of the equation.
-1.108333334 + 1.108333334 + x = 1.166934494 + 1.108333334

Combine like terms: -1.108333334 + 1.108333334 = 0.000000000
0.000000000 + x = 1.166934494 + 1.108333334
x = 1.166934494 + 1.108333334

Combine like terms: 1.166934494 + 1.108333334 = 2.275267828
x = 2.275267828

Simplifying
x = 2.275267828

Subproblem 2
x + -1.108333334 = -1.166934494

Simplifying
x + -1.108333334 = -1.166934494

Reorder the terms:
-1.108333334 + x = -1.166934494

Solving
-1.108333334 + x = -1.166934494

Solving for variable 'x'.

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

Add '1.108333334' to each side of the equation.
-1.108333334 + 1.108333334 + x = -1.166934494 + 1.108333334

Combine like terms: -1.108333334 + 1.108333334 = 0.000000000
0.000000000 + x = -1.166934494 + 1.108333334
x = -1.166934494 + 1.108333334

Combine like terms: -1.166934494 + 1.108333334 = -0.05860116
x = -0.05860116

Simplifying
x = -0.05860116

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.275267828, -0.05860116}
Solution
x = {2.275267828, -0.05860116}