14x^2+14=60x-12

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

Simplifying
14x2 + 14 = 60x + -12

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

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

Solving
14 + 14x2 = -12 + 60x

Solving for variable 'x'.

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

Combine like terms: 14 + 12 = 26
26 + -60x + 14x2 = -12 + 60x + 12 + -60x

Reorder the terms:
26 + -60x + 14x2 = -12 + 12 + 60x + -60x

Combine like terms: -12 + 12 = 0
26 + -60x + 14x2 = 0 + 60x + -60x
26 + -60x + 14x2 = 60x + -60x

Combine like terms: 60x + -60x = 0
26 + -60x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + -30x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(13 + -30x + 7x2)' equal to zero and attempt to solve:

Simplifying
13 + -30x + 7x2 = 0

Solving
13 + -30x + 7x2 = 0

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

Divide each side by '7'.
1.857142857 + -4.285714286x + x2 = 0

Move the constant term to the right:

Add '-1.857142857' to each side of the equation.
1.857142857 + -4.285714286x + -1.857142857 + x2 = 0 + -1.857142857

Reorder the terms:
1.857142857 + -1.857142857 + -4.285714286x + x2 = 0 + -1.857142857

Combine like terms: 1.857142857 + -1.857142857 = 0.000000000
0.000000000 + -4.285714286x + x2 = 0 + -1.857142857
-4.285714286x + x2 = 0 + -1.857142857

Combine like terms: 0 + -1.857142857 = -1.857142857
-4.285714286x + x2 = -1.857142857

The x term is -4.285714286x.  Take half its coefficient (-2.142857143).
Square it (4.591836735) and add it to both sides.

Add '4.591836735' to each side of the equation.
-4.285714286x + 4.591836735 + x2 = -1.857142857 + 4.591836735

Reorder the terms:
4.591836735 + -4.285714286x + x2 = -1.857142857 + 4.591836735

Combine like terms: -1.857142857 + 4.591836735 = 2.734693878
4.591836735 + -4.285714286x + x2 = 2.734693878

Factor a perfect square on the left side:
(x + -2.142857143)(x + -2.142857143) = 2.734693878

Calculate the square root of the right side: 1.653690986

Break this problem into two subproblems by setting 
(x + -2.142857143) equal to 1.653690986 and -1.653690986.

Subproblem 1
x + -2.142857143 = 1.653690986

Simplifying
x + -2.142857143 = 1.653690986

Reorder the terms:
-2.142857143 + x = 1.653690986

Solving
-2.142857143 + x = 1.653690986

Solving for variable 'x'.

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

Add '2.142857143' to each side of the equation.
-2.142857143 + 2.142857143 + x = 1.653690986 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + x = 1.653690986 + 2.142857143
x = 1.653690986 + 2.142857143

Combine like terms: 1.653690986 + 2.142857143 = 3.796548129
x = 3.796548129

Simplifying
x = 3.796548129

Subproblem 2
x + -2.142857143 = -1.653690986

Simplifying
x + -2.142857143 = -1.653690986

Reorder the terms:
-2.142857143 + x = -1.653690986

Solving
-2.142857143 + x = -1.653690986

Solving for variable 'x'.

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

Add '2.142857143' to each side of the equation.
-2.142857143 + 2.142857143 + x = -1.653690986 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + x = -1.653690986 + 2.142857143
x = -1.653690986 + 2.142857143

Combine like terms: -1.653690986 + 2.142857143 = 0.489166157
x = 0.489166157

Simplifying
x = 0.489166157

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.796548129, 0.489166157}
Solution
x = {3.796548129, 0.489166157}