12x^2-40x-7=6x-1

Solution for 12x^2-40x-7=6x-1 equation:

Simplifying
12x2 + -40x + -7 = 6x + -1

Reorder the terms:
-7 + -40x + 12x2 = 6x + -1

Reorder the terms:
-7 + -40x + 12x2 = -1 + 6x

Solving
-7 + -40x + 12x2 = -1 + 6x

Solving for variable 'x'.

Reorder the terms:
-7 + 1 + -40x + -6x + 12x2 = -1 + 6x + 1 + -6x

Combine like terms: -7 + 1 = -6
-6 + -40x + -6x + 12x2 = -1 + 6x + 1 + -6x

Combine like terms: -40x + -6x = -46x
-6 + -46x + 12x2 = -1 + 6x + 1 + -6x

Reorder the terms:
-6 + -46x + 12x2 = -1 + 1 + 6x + -6x

Combine like terms: -1 + 1 = 0
-6 + -46x + 12x2 = 0 + 6x + -6x
-6 + -46x + 12x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6 + -46x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -23x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -23x + 6x2)' equal to zero and attempt to solve:

Simplifying
-3 + -23x + 6x2 = 0

Solving
-3 + -23x + 6x2 = 0

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

Divide each side by '6'.
-0.5 + -3.833333333x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -3.833333333x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -3.833333333x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -3.833333333x + x2 = 0 + 0.5
-3.833333333x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-3.833333333x + x2 = 0.5

The x term is -3.833333333x.  Take half its coefficient (-1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
-3.833333333x + 3.673611112 + x2 = 0.5 + 3.673611112

Reorder the terms:
3.673611112 + -3.833333333x + x2 = 0.5 + 3.673611112

Combine like terms: 0.5 + 3.673611112 = 4.173611112
3.673611112 + -3.833333333x + x2 = 4.173611112

Factor a perfect square on the left side:
(x + -1.916666667)(x + -1.916666667) = 4.173611112

Calculate the square root of the right side: 2.042941779

Break this problem into two subproblems by setting 
(x + -1.916666667) equal to 2.042941779 and -2.042941779.

Subproblem 1
x + -1.916666667 = 2.042941779

Simplifying
x + -1.916666667 = 2.042941779

Reorder the terms:
-1.916666667 + x = 2.042941779

Solving
-1.916666667 + x = 2.042941779

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = 2.042941779 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = 2.042941779 + 1.916666667
x = 2.042941779 + 1.916666667

Combine like terms: 2.042941779 + 1.916666667 = 3.959608446
x = 3.959608446

Simplifying
x = 3.959608446

Subproblem 2
x + -1.916666667 = -2.042941779

Simplifying
x + -1.916666667 = -2.042941779

Reorder the terms:
-1.916666667 + x = -2.042941779

Solving
-1.916666667 + x = -2.042941779

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = -2.042941779 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = -2.042941779 + 1.916666667
x = -2.042941779 + 1.916666667

Combine like terms: -2.042941779 + 1.916666667 = -0.126275112
x = -0.126275112

Simplifying
x = -0.126275112

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.959608446, -0.126275112}
Solution
x = {3.959608446, -0.126275112}