-3(x-2)7x=9x-3

Solution for -3(x-2)7x=9x-3 equation:

Simplifying
-3(x + -2) * 7x = 9x + -3

Reorder the terms:
-3(-2 + x) * 7x = 9x + -3

Reorder the terms for easier multiplication:
-3 * 7x(-2 + x) = 9x + -3

Multiply -3 * 7
-21x(-2 + x) = 9x + -3
(-2 * -21x + x * -21x) = 9x + -3
(42x + -21x2) = 9x + -3

Reorder the terms:
42x + -21x2 = -3 + 9x

Solving
42x + -21x2 = -3 + 9x

Solving for variable 'x'.

Reorder the terms:
3 + 42x + -9x + -21x2 = -3 + 9x + 3 + -9x

Combine like terms: 42x + -9x = 33x
3 + 33x + -21x2 = -3 + 9x + 3 + -9x

Reorder the terms:
3 + 33x + -21x2 = -3 + 3 + 9x + -9x

Combine like terms: -3 + 3 = 0
3 + 33x + -21x2 = 0 + 9x + -9x
3 + 33x + -21x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
3 + 33x + -21x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 11x + -7x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 11x + -7x2)' equal to zero and attempt to solve:

Simplifying
1 + 11x + -7x2 = 0

Solving
1 + 11x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.1428571429 + -1.571428571x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -1.571428571x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -1.571428571x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -1.571428571x + x2 = 0 + 0.1428571429
-1.571428571x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-1.571428571x + x2 = 0.1428571429

The x term is -1.571428571x.  Take half its coefficient (-0.7857142855).
Square it (0.6173469384) and add it to both sides.

Add '0.6173469384' to each side of the equation.
-1.571428571x + 0.6173469384 + x2 = 0.1428571429 + 0.6173469384

Reorder the terms:
0.6173469384 + -1.571428571x + x2 = 0.1428571429 + 0.6173469384

Combine like terms: 0.1428571429 + 0.6173469384 = 0.7602040813
0.6173469384 + -1.571428571x + x2 = 0.7602040813

Factor a perfect square on the left side:
(x + -0.7857142855)(x + -0.7857142855) = 0.7602040813

Calculate the square root of the right side: 0.87189683

Break this problem into two subproblems by setting 
(x + -0.7857142855) equal to 0.87189683 and -0.87189683.

Subproblem 1
x + -0.7857142855 = 0.87189683

Simplifying
x + -0.7857142855 = 0.87189683

Reorder the terms:
-0.7857142855 + x = 0.87189683

Solving
-0.7857142855 + x = 0.87189683

Solving for variable 'x'.

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

Add '0.7857142855' to each side of the equation.
-0.7857142855 + 0.7857142855 + x = 0.87189683 + 0.7857142855

Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000
0.0000000000 + x = 0.87189683 + 0.7857142855
x = 0.87189683 + 0.7857142855

Combine like terms: 0.87189683 + 0.7857142855 = 1.6576111155
x = 1.6576111155

Simplifying
x = 1.6576111155

Subproblem 2
x + -0.7857142855 = -0.87189683

Simplifying
x + -0.7857142855 = -0.87189683

Reorder the terms:
-0.7857142855 + x = -0.87189683

Solving
-0.7857142855 + x = -0.87189683

Solving for variable 'x'.

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

Add '0.7857142855' to each side of the equation.
-0.7857142855 + 0.7857142855 + x = -0.87189683 + 0.7857142855

Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000
0.0000000000 + x = -0.87189683 + 0.7857142855
x = -0.87189683 + 0.7857142855

Combine like terms: -0.87189683 + 0.7857142855 = -0.0861825445
x = -0.0861825445

Simplifying
x = -0.0861825445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6576111155, -0.0861825445}
Solution
x = {1.6576111155, -0.0861825445}