14x^2-14x=60x-12

Solution for 14x^2-14x=60x-12 equation:

Simplifying
14x2 + -14x = 60x + -12

Reorder the terms:
-14x + 14x2 = 60x + -12

Reorder the terms:
-14x + 14x2 = -12 + 60x

Solving
-14x + 14x2 = -12 + 60x

Solving for variable 'x'.

Reorder the terms:
12 + -14x + -60x + 14x2 = -12 + 60x + 12 + -60x

Combine like terms: -14x + -60x = -74x
12 + -74x + 14x2 = -12 + 60x + 12 + -60x

Reorder the terms:
12 + -74x + 14x2 = -12 + 12 + 60x + -60x

Combine like terms: -12 + 12 = 0
12 + -74x + 14x2 = 0 + 60x + -60x
12 + -74x + 14x2 = 60x + -60x

Combine like terms: 60x + -60x = 0
12 + -74x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -37x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -37x + 7x2)' equal to zero and attempt to solve:

Simplifying
6 + -37x + 7x2 = 0

Solving
6 + -37x + 7x2 = 0

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

Divide each side by '7'.
0.8571428571 + -5.285714286x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + -5.285714286x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + -5.285714286x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + -5.285714286x + x2 = 0 + -0.8571428571
-5.285714286x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
-5.285714286x + x2 = -0.8571428571

The x term is -5.285714286x.  Take half its coefficient (-2.642857143).
Square it (6.984693878) and add it to both sides.

Add '6.984693878' to each side of the equation.
-5.285714286x + 6.984693878 + x2 = -0.8571428571 + 6.984693878

Reorder the terms:
6.984693878 + -5.285714286x + x2 = -0.8571428571 + 6.984693878

Combine like terms: -0.8571428571 + 6.984693878 = 6.1275510209
6.984693878 + -5.285714286x + x2 = 6.1275510209

Factor a perfect square on the left side:
(x + -2.642857143)(x + -2.642857143) = 6.1275510209

Calculate the square root of the right side: 2.475389065

Break this problem into two subproblems by setting 
(x + -2.642857143) equal to 2.475389065 and -2.475389065.

Subproblem 1
x + -2.642857143 = 2.475389065

Simplifying
x + -2.642857143 = 2.475389065

Reorder the terms:
-2.642857143 + x = 2.475389065

Solving
-2.642857143 + x = 2.475389065

Solving for variable 'x'.

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

Add '2.642857143' to each side of the equation.
-2.642857143 + 2.642857143 + x = 2.475389065 + 2.642857143

Combine like terms: -2.642857143 + 2.642857143 = 0.000000000
0.000000000 + x = 2.475389065 + 2.642857143
x = 2.475389065 + 2.642857143

Combine like terms: 2.475389065 + 2.642857143 = 5.118246208
x = 5.118246208

Simplifying
x = 5.118246208

Subproblem 2
x + -2.642857143 = -2.475389065

Simplifying
x + -2.642857143 = -2.475389065

Reorder the terms:
-2.642857143 + x = -2.475389065

Solving
-2.642857143 + x = -2.475389065

Solving for variable 'x'.

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

Add '2.642857143' to each side of the equation.
-2.642857143 + 2.642857143 + x = -2.475389065 + 2.642857143

Combine like terms: -2.642857143 + 2.642857143 = 0.000000000
0.000000000 + x = -2.475389065 + 2.642857143
x = -2.475389065 + 2.642857143

Combine like terms: -2.475389065 + 2.642857143 = 0.167468078
x = 0.167468078

Simplifying
x = 0.167468078

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.118246208, 0.167468078}
Solution
x = {5.118246208, 0.167468078}