(6x-7)(2x)(103)=180

Solution for (6x-7)(2x)(103)=180 equation:

Simplifying
(6x + -7)(2x)(103) = 180

Reorder the terms:
(-7 + 6x)(2x)(103) = 180

Remove parenthesis around (2x)
(-7 + 6x) * 2x(103) = 180

Reorder the terms for easier multiplication:
2 * 103x(-7 + 6x) = 180

Multiply 2 * 103
206x(-7 + 6x) = 180
(-7 * 206x + 6x * 206x) = 180
(-1442x + 1236x2) = 180

Solving
-1442x + 1236x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -1442x + 1236x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -1442x + 1236x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + -721x + 618x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-90 + -721x + 618x2)' equal to zero and attempt to solve:

Simplifying
-90 + -721x + 618x2 = 0

Solving
-90 + -721x + 618x2 = 0

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

Divide each side by '618'.
-0.145631068 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '0.145631068' to each side of the equation.
-0.145631068 + -1.166666667x + 0.145631068 + x2 = 0 + 0.145631068

Reorder the terms:
-0.145631068 + 0.145631068 + -1.166666667x + x2 = 0 + 0.145631068

Combine like terms: -0.145631068 + 0.145631068 = 0.000000000
0.000000000 + -1.166666667x + x2 = 0 + 0.145631068
-1.166666667x + x2 = 0 + 0.145631068

Combine like terms: 0 + 0.145631068 = 0.145631068
-1.166666667x + x2 = 0.145631068

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = 0.145631068 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = 0.145631068 + 0.3402777780

Combine like terms: 0.145631068 + 0.3402777780 = 0.485908846
0.3402777780 + -1.166666667x + x2 = 0.485908846

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 0.485908846

Calculate the square root of the right side: 0.697071622

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 0.697071622 and -0.697071622.

Subproblem 1
x + -0.5833333335 = 0.697071622

Simplifying
x + -0.5833333335 = 0.697071622

Reorder the terms:
-0.5833333335 + x = 0.697071622

Solving
-0.5833333335 + x = 0.697071622

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = 0.697071622 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = 0.697071622 + 0.5833333335
x = 0.697071622 + 0.5833333335

Combine like terms: 0.697071622 + 0.5833333335 = 1.2804049555
x = 1.2804049555

Simplifying
x = 1.2804049555

Subproblem 2
x + -0.5833333335 = -0.697071622

Simplifying
x + -0.5833333335 = -0.697071622

Reorder the terms:
-0.5833333335 + x = -0.697071622

Solving
-0.5833333335 + x = -0.697071622

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = -0.697071622 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = -0.697071622 + 0.5833333335
x = -0.697071622 + 0.5833333335

Combine like terms: -0.697071622 + 0.5833333335 = -0.1137382885
x = -0.1137382885

Simplifying
x = -0.1137382885

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2804049555, -0.1137382885}
Solution
x = {1.2804049555, -0.1137382885}