-2x(x-18)+(x+3)=x+14

Solution for -2x(x-18)+(x+3)=x+14 equation:

Simplifying
-2x(x + -18) + (x + 3) = x + 14

Reorder the terms:
-2x(-18 + x) + (x + 3) = x + 14
(-18 * -2x + x * -2x) + (x + 3) = x + 14
(36x + -2x2) + (x + 3) = x + 14

Reorder the terms:
36x + -2x2 + (3 + x) = x + 14

Remove parenthesis around (3 + x)
36x + -2x2 + 3 + x = x + 14

Reorder the terms:
3 + 36x + x + -2x2 = x + 14

Combine like terms: 36x + x = 37x
3 + 37x + -2x2 = x + 14

Reorder the terms:
3 + 37x + -2x2 = 14 + x

Solving
3 + 37x + -2x2 = 14 + x

Solving for variable 'x'.

Reorder the terms:
3 + -14 + 37x + -1x + -2x2 = 14 + x + -14 + -1x

Combine like terms: 3 + -14 = -11
-11 + 37x + -1x + -2x2 = 14 + x + -14 + -1x

Combine like terms: 37x + -1x = 36x
-11 + 36x + -2x2 = 14 + x + -14 + -1x

Reorder the terms:
-11 + 36x + -2x2 = 14 + -14 + x + -1x

Combine like terms: 14 + -14 = 0
-11 + 36x + -2x2 = 0 + x + -1x
-11 + 36x + -2x2 = x + -1x

Combine like terms: x + -1x = 0
-11 + 36x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
5.5 + -18x + x2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -18x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -18x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -18x + x2 = 0 + -5.5
-18x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-18x + x2 = -5.5

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -5.5 + 81

Reorder the terms:
81 + -18x + x2 = -5.5 + 81

Combine like terms: -5.5 + 81 = 75.5
81 + -18x + x2 = 75.5

Factor a perfect square on the left side:
(x + -9)(x + -9) = 75.5

Calculate the square root of the right side: 8.689073598

Break this problem into two subproblems by setting 
(x + -9) equal to 8.689073598 and -8.689073598.

Subproblem 1
x + -9 = 8.689073598

Simplifying
x + -9 = 8.689073598

Reorder the terms:
-9 + x = 8.689073598

Solving
-9 + x = 8.689073598

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 8.689073598 + 9

Combine like terms: -9 + 9 = 0
0 + x = 8.689073598 + 9
x = 8.689073598 + 9

Combine like terms: 8.689073598 + 9 = 17.689073598
x = 17.689073598

Simplifying
x = 17.689073598

Subproblem 2
x + -9 = -8.689073598

Simplifying
x + -9 = -8.689073598

Reorder the terms:
-9 + x = -8.689073598

Solving
-9 + x = -8.689073598

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -8.689073598 + 9

Combine like terms: -9 + 9 = 0
0 + x = -8.689073598 + 9
x = -8.689073598 + 9

Combine like terms: -8.689073598 + 9 = 0.310926402
x = 0.310926402

Simplifying
x = 0.310926402

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.689073598, 0.310926402}