6x(7x-8)-2(21x-6)=3-30x

Solution for 6x(7x-8)-2(21x-6)=3-30x equation:

Simplifying
6x(7x + -8) + -2(21x + -6) = 3 + -30x

Reorder the terms:
6x(-8 + 7x) + -2(21x + -6) = 3 + -30x
(-8 * 6x + 7x * 6x) + -2(21x + -6) = 3 + -30x
(-48x + 42x2) + -2(21x + -6) = 3 + -30x

Reorder the terms:
-48x + 42x2 + -2(-6 + 21x) = 3 + -30x
-48x + 42x2 + (-6 * -2 + 21x * -2) = 3 + -30x
-48x + 42x2 + (12 + -42x) = 3 + -30x

Reorder the terms:
12 + -48x + -42x + 42x2 = 3 + -30x

Combine like terms: -48x + -42x = -90x
12 + -90x + 42x2 = 3 + -30x

Solving
12 + -90x + 42x2 = 3 + -30x

Solving for variable 'x'.

Reorder the terms:
12 + -3 + -90x + 30x + 42x2 = 3 + -30x + -3 + 30x

Combine like terms: 12 + -3 = 9
9 + -90x + 30x + 42x2 = 3 + -30x + -3 + 30x

Combine like terms: -90x + 30x = -60x
9 + -60x + 42x2 = 3 + -30x + -3 + 30x

Reorder the terms:
9 + -60x + 42x2 = 3 + -3 + -30x + 30x

Combine like terms: 3 + -3 = 0
9 + -60x + 42x2 = 0 + -30x + 30x
9 + -60x + 42x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
9 + -60x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -20x + 14x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -20x + 14x2)' equal to zero and attempt to solve:

Simplifying
3 + -20x + 14x2 = 0

Solving
3 + -20x + 14x2 = 0

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

Divide each side by '14'.
0.2142857143 + -1.428571429x + x2 = 0

Move the constant term to the right:

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -1.428571429x + -0.2142857143 + x2 = 0 + -0.2142857143

Reorder the terms:
0.2142857143 + -0.2142857143 + -1.428571429x + x2 = 0 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + -1.428571429x + x2 = 0 + -0.2142857143
-1.428571429x + x2 = 0 + -0.2142857143

Combine like terms: 0 + -0.2142857143 = -0.2142857143
-1.428571429x + x2 = -0.2142857143

The x term is -1.428571429x.  Take half its coefficient (-0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
-1.428571429x + 0.5102040819 + x2 = -0.2142857143 + 0.5102040819

Reorder the terms:
0.5102040819 + -1.428571429x + x2 = -0.2142857143 + 0.5102040819

Combine like terms: -0.2142857143 + 0.5102040819 = 0.2959183676
0.5102040819 + -1.428571429x + x2 = 0.2959183676

Factor a perfect square on the left side:
(x + -0.7142857145)(x + -0.7142857145) = 0.2959183676

Calculate the square root of the right side: 0.543983794

Break this problem into two subproblems by setting 
(x + -0.7142857145) equal to 0.543983794 and -0.543983794.

Subproblem 1
x + -0.7142857145 = 0.543983794

Simplifying
x + -0.7142857145 = 0.543983794

Reorder the terms:
-0.7142857145 + x = 0.543983794

Solving
-0.7142857145 + x = 0.543983794

Solving for variable 'x'.

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

Add '0.7142857145' to each side of the equation.
-0.7142857145 + 0.7142857145 + x = 0.543983794 + 0.7142857145

Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000
0.0000000000 + x = 0.543983794 + 0.7142857145
x = 0.543983794 + 0.7142857145

Combine like terms: 0.543983794 + 0.7142857145 = 1.2582695085
x = 1.2582695085

Simplifying
x = 1.2582695085

Subproblem 2
x + -0.7142857145 = -0.543983794

Simplifying
x + -0.7142857145 = -0.543983794

Reorder the terms:
-0.7142857145 + x = -0.543983794

Solving
-0.7142857145 + x = -0.543983794

Solving for variable 'x'.

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

Add '0.7142857145' to each side of the equation.
-0.7142857145 + 0.7142857145 + x = -0.543983794 + 0.7142857145

Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000
0.0000000000 + x = -0.543983794 + 0.7142857145
x = -0.543983794 + 0.7142857145

Combine like terms: -0.543983794 + 0.7142857145 = 0.1703019205
x = 0.1703019205

Simplifying
x = 0.1703019205

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2582695085, 0.1703019205}
Solution
x = {1.2582695085, 0.1703019205}