6x(x+26)-62=2(x+150)+37

Solution for 6x(x+26)-62=2(x+150)+37 equation:

Simplifying
6x(x + 26) + -62 = 2(x + 150) + 37

Reorder the terms:
6x(26 + x) + -62 = 2(x + 150) + 37
(26 * 6x + x * 6x) + -62 = 2(x + 150) + 37
(156x + 6x2) + -62 = 2(x + 150) + 37

Reorder the terms:
-62 + 156x + 6x2 = 2(x + 150) + 37

Reorder the terms:
-62 + 156x + 6x2 = 2(150 + x) + 37
-62 + 156x + 6x2 = (150 * 2 + x * 2) + 37
-62 + 156x + 6x2 = (300 + 2x) + 37

Reorder the terms:
-62 + 156x + 6x2 = 300 + 37 + 2x

Combine like terms: 300 + 37 = 337
-62 + 156x + 6x2 = 337 + 2x

Solving
-62 + 156x + 6x2 = 337 + 2x

Solving for variable 'x'.

Reorder the terms:
-62 + -337 + 156x + -2x + 6x2 = 337 + 2x + -337 + -2x

Combine like terms: -62 + -337 = -399
-399 + 156x + -2x + 6x2 = 337 + 2x + -337 + -2x

Combine like terms: 156x + -2x = 154x
-399 + 154x + 6x2 = 337 + 2x + -337 + -2x

Reorder the terms:
-399 + 154x + 6x2 = 337 + -337 + 2x + -2x

Combine like terms: 337 + -337 = 0
-399 + 154x + 6x2 = 0 + 2x + -2x
-399 + 154x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-399 + 154x + 6x2 = 0

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

Divide each side by '6'.
-66.5 + 25.66666667x + x2 = 0

Move the constant term to the right:

Add '66.5' to each side of the equation.
-66.5 + 25.66666667x + 66.5 + x2 = 0 + 66.5

Reorder the terms:
-66.5 + 66.5 + 25.66666667x + x2 = 0 + 66.5

Combine like terms: -66.5 + 66.5 = 0.0
0.0 + 25.66666667x + x2 = 0 + 66.5
25.66666667x + x2 = 0 + 66.5

Combine like terms: 0 + 66.5 = 66.5
25.66666667x + x2 = 66.5

The x term is 25.66666667x.  Take half its coefficient (12.83333334).
Square it (164.6944446) and add it to both sides.

Add '164.6944446' to each side of the equation.
25.66666667x + 164.6944446 + x2 = 66.5 + 164.6944446

Reorder the terms:
164.6944446 + 25.66666667x + x2 = 66.5 + 164.6944446

Combine like terms: 66.5 + 164.6944446 = 231.1944446
164.6944446 + 25.66666667x + x2 = 231.1944446

Factor a perfect square on the left side:
(x + 12.83333334)(x + 12.83333334) = 231.1944446

Calculate the square root of the right side: 15.205079566

Break this problem into two subproblems by setting 
(x + 12.83333334) equal to 15.205079566 and -15.205079566.

Subproblem 1
x + 12.83333334 = 15.205079566

Simplifying
x + 12.83333334 = 15.205079566

Reorder the terms:
12.83333334 + x = 15.205079566

Solving
12.83333334 + x = 15.205079566

Solving for variable 'x'.

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

Add '-12.83333334' to each side of the equation.
12.83333334 + -12.83333334 + x = 15.205079566 + -12.83333334

Combine like terms: 12.83333334 + -12.83333334 = 0.00000000
0.00000000 + x = 15.205079566 + -12.83333334
x = 15.205079566 + -12.83333334

Combine like terms: 15.205079566 + -12.83333334 = 2.371746226
x = 2.371746226

Simplifying
x = 2.371746226

Subproblem 2
x + 12.83333334 = -15.205079566

Simplifying
x + 12.83333334 = -15.205079566

Reorder the terms:
12.83333334 + x = -15.205079566

Solving
12.83333334 + x = -15.205079566

Solving for variable 'x'.

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

Add '-12.83333334' to each side of the equation.
12.83333334 + -12.83333334 + x = -15.205079566 + -12.83333334

Combine like terms: 12.83333334 + -12.83333334 = 0.00000000
0.00000000 + x = -15.205079566 + -12.83333334
x = -15.205079566 + -12.83333334

Combine like terms: -15.205079566 + -12.83333334 = -28.038412906
x = -28.038412906

Simplifying
x = -28.038412906

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.371746226, -28.038412906}