5x^2-(x+1)(-6x+2)=12

Solution for 5x^2-(x+1)(-6x+2)=12 equation:

Simplifying
5x2 + -1(x + 1)(-6x + 2) = 12

Reorder the terms:
5x2 + -1(1 + x)(-6x + 2) = 12

Reorder the terms:
5x2 + -1(1 + x)(2 + -6x) = 12

Multiply (1 + x) * (2 + -6x)
5x2 + -1(1(2 + -6x) + x(2 + -6x)) = 12
5x2 + -1((2 * 1 + -6x * 1) + x(2 + -6x)) = 12
5x2 + -1((2 + -6x) + x(2 + -6x)) = 12
5x2 + -1(2 + -6x + (2 * x + -6x * x)) = 12
5x2 + -1(2 + -6x + (2x + -6x2)) = 12

Combine like terms: -6x + 2x = -4x
5x2 + -1(2 + -4x + -6x2) = 12
5x2 + (2 * -1 + -4x * -1 + -6x2 * -1) = 12
5x2 + (-2 + 4x + 6x2) = 12

Reorder the terms:
-2 + 4x + 5x2 + 6x2 = 12

Combine like terms: 5x2 + 6x2 = 11x2
-2 + 4x + 11x2 = 12

Solving
-2 + 4x + 11x2 = 12

Solving for variable 'x'.

Reorder the terms:
-2 + -12 + 4x + 11x2 = 12 + -12

Combine like terms: -2 + -12 = -14
-14 + 4x + 11x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-14 + 4x + 11x2 = 0

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

Divide each side by '11'.
-1.272727273 + 0.3636363636x + x2 = 0

Move the constant term to the right:

Add '1.272727273' to each side of the equation.
-1.272727273 + 0.3636363636x + 1.272727273 + x2 = 0 + 1.272727273

Reorder the terms:
-1.272727273 + 1.272727273 + 0.3636363636x + x2 = 0 + 1.272727273

Combine like terms: -1.272727273 + 1.272727273 = 0.000000000
0.000000000 + 0.3636363636x + x2 = 0 + 1.272727273
0.3636363636x + x2 = 0 + 1.272727273

Combine like terms: 0 + 1.272727273 = 1.272727273
0.3636363636x + x2 = 1.272727273

The x term is 0.3636363636x.  Take half its coefficient (0.1818181818).
Square it (0.03305785123) and add it to both sides.

Add '0.03305785123' to each side of the equation.
0.3636363636x + 0.03305785123 + x2 = 1.272727273 + 0.03305785123

Reorder the terms:
0.03305785123 + 0.3636363636x + x2 = 1.272727273 + 0.03305785123

Combine like terms: 1.272727273 + 0.03305785123 = 1.30578512423
0.03305785123 + 0.3636363636x + x2 = 1.30578512423

Factor a perfect square on the left side:
(x + 0.1818181818)(x + 0.1818181818) = 1.30578512423

Calculate the square root of the right side: 1.142709554

Break this problem into two subproblems by setting 
(x + 0.1818181818) equal to 1.142709554 and -1.142709554.

Subproblem 1
x + 0.1818181818 = 1.142709554

Simplifying
x + 0.1818181818 = 1.142709554

Reorder the terms:
0.1818181818 + x = 1.142709554

Solving
0.1818181818 + x = 1.142709554

Solving for variable 'x'.

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

Add '-0.1818181818' to each side of the equation.
0.1818181818 + -0.1818181818 + x = 1.142709554 + -0.1818181818

Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000
0.0000000000 + x = 1.142709554 + -0.1818181818
x = 1.142709554 + -0.1818181818

Combine like terms: 1.142709554 + -0.1818181818 = 0.9608913722
x = 0.9608913722

Simplifying
x = 0.9608913722

Subproblem 2
x + 0.1818181818 = -1.142709554

Simplifying
x + 0.1818181818 = -1.142709554

Reorder the terms:
0.1818181818 + x = -1.142709554

Solving
0.1818181818 + x = -1.142709554

Solving for variable 'x'.

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

Add '-0.1818181818' to each side of the equation.
0.1818181818 + -0.1818181818 + x = -1.142709554 + -0.1818181818

Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000
0.0000000000 + x = -1.142709554 + -0.1818181818
x = -1.142709554 + -0.1818181818

Combine like terms: -1.142709554 + -0.1818181818 = -1.3245277358
x = -1.3245277358

Simplifying
x = -1.3245277358

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9608913722, -1.3245277358}