18=6x(x-13)

Solution for 18=6x(x-13) equation:

Simplifying
18 = 6x(x + -13)

Reorder the terms:
18 = 6x(-13 + x)
18 = (-13 * 6x + x * 6x)
18 = (-78x + 6x2)

Solving
18 = -78x + 6x2

Solving for variable 'x'.

Reorder the terms:
18 + 78x + -6x2 = -78x + 78x + 6x2 + -6x2

Combine like terms: -78x + 78x = 0
18 + 78x + -6x2 = 0 + 6x2 + -6x2
18 + 78x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
18 + 78x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 13x + -1x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + 13x + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + 13x + -1x2 = 0

Solving
3 + 13x + -1x2 = 0

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

Divide each side by '-1'.
-3 + -13x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -13x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -13x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -13x + x2 = 0 + 3
-13x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-13x + x2 = 3

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 3 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 3 + 42.25

Combine like terms: 3 + 42.25 = 45.25
42.25 + -13x + x2 = 45.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(x + -6.5) equal to 6.726812024 and -6.726812024.

Subproblem 1
x + -6.5 = 6.726812024

Simplifying
x + -6.5 = 6.726812024

Reorder the terms:
-6.5 + x = 6.726812024

Solving
-6.5 + x = 6.726812024

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 6.726812024 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 6.726812024 + 6.5
x = 6.726812024 + 6.5

Combine like terms: 6.726812024 + 6.5 = 13.226812024
x = 13.226812024

Simplifying
x = 13.226812024

Subproblem 2
x + -6.5 = -6.726812024

Simplifying
x + -6.5 = -6.726812024

Reorder the terms:
-6.5 + x = -6.726812024

Solving
-6.5 + x = -6.726812024

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -6.726812024 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -6.726812024 + 6.5
x = -6.726812024 + 6.5

Combine like terms: -6.726812024 + 6.5 = -0.226812024
x = -0.226812024

Simplifying
x = -0.226812024

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.226812024, -0.226812024}
Solution
x = {13.226812024, -0.226812024}