2x+18=2(x^2-5x)

Solution for 2x+18=2(x^2-5x) equation:

Simplifying
2x + 18 = 2(x2 + -5x)

Reorder the terms:
18 + 2x = 2(x2 + -5x)

Reorder the terms:
18 + 2x = 2(-5x + x2)
18 + 2x = (-5x * 2 + x2 * 2)
18 + 2x = (-10x + 2x2)

Solving
18 + 2x = -10x + 2x2

Solving for variable 'x'.

Combine like terms: 2x + 10x = 12x
18 + 12x + -2x2 = -10x + 2x2 + 10x + -2x2

Reorder the terms:
18 + 12x + -2x2 = -10x + 10x + 2x2 + -2x2

Combine like terms: -10x + 10x = 0
18 + 12x + -2x2 = 0 + 2x2 + -2x2
18 + 12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
18 + 12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 6x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + 6x + -1x2)' equal to zero and attempt to solve:

Simplifying
9 + 6x + -1x2 = 0

Solving
9 + 6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-9 + -6x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -6x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -6x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -6x + x2 = 0 + 9
-6x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-6x + x2 = 9

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 9 + 9

Reorder the terms:
9 + -6x + x2 = 9 + 9

Combine like terms: 9 + 9 = 18
9 + -6x + x2 = 18

Factor a perfect square on the left side:
(x + -3)(x + -3) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -3) equal to 4.242640687 and -4.242640687.

Subproblem 1
x + -3 = 4.242640687

Simplifying
x + -3 = 4.242640687

Reorder the terms:
-3 + x = 4.242640687

Solving
-3 + x = 4.242640687

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 4.242640687 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.242640687 + 3
x = 4.242640687 + 3

Combine like terms: 4.242640687 + 3 = 7.242640687
x = 7.242640687

Simplifying
x = 7.242640687

Subproblem 2
x + -3 = -4.242640687

Simplifying
x + -3 = -4.242640687

Reorder the terms:
-3 + x = -4.242640687

Solving
-3 + x = -4.242640687

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -4.242640687 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.242640687 + 3
x = -4.242640687 + 3

Combine like terms: -4.242640687 + 3 = -1.242640687
x = -1.242640687

Simplifying
x = -1.242640687

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.242640687, -1.242640687}
Solution
x = {7.242640687, -1.242640687}