54x=(x+3)(x-3)

Solution for 54x=(x+3)(x-3) equation:

Simplifying
54x = (x + 3)(x + -3)

Reorder the terms:
54x = (3 + x)(x + -3)

Reorder the terms:
54x = (3 + x)(-3 + x)

Multiply (3 + x) * (-3 + x)
54x = (3(-3 + x) + x(-3 + x))
54x = ((-3 * 3 + x * 3) + x(-3 + x))
54x = ((-9 + 3x) + x(-3 + x))
54x = (-9 + 3x + (-3 * x + x * x))
54x = (-9 + 3x + (-3x + x2))

Combine like terms: 3x + -3x = 0
54x = (-9 + 0 + x2)
54x = (-9 + x2)

Solving
54x = -9 + x2

Solving for variable 'x'.

Reorder the terms:
9 + 54x + -1x2 = -9 + x2 + 9 + -1x2

Reorder the terms:
9 + 54x + -1x2 = -9 + 9 + x2 + -1x2

Combine like terms: -9 + 9 = 0
9 + 54x + -1x2 = 0 + x2 + -1x2
9 + 54x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9 + 54x + -1x2 = 0

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

Divide each side by '-1'.
-9 + -54x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -54x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -54x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -54x + x2 = 0 + 9
-54x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-54x + x2 = 9

The x term is -54x.  Take half its coefficient (-27).
Square it (729) and add it to both sides.

Add '729' to each side of the equation.
-54x + 729 + x2 = 9 + 729

Reorder the terms:
729 + -54x + x2 = 9 + 729

Combine like terms: 9 + 729 = 738
729 + -54x + x2 = 738

Factor a perfect square on the left side:
(x + -27)(x + -27) = 738

Calculate the square root of the right side: 27.166155414

Break this problem into two subproblems by setting 
(x + -27) equal to 27.166155414 and -27.166155414.

Subproblem 1
x + -27 = 27.166155414

Simplifying
x + -27 = 27.166155414

Reorder the terms:
-27 + x = 27.166155414

Solving
-27 + x = 27.166155414

Solving for variable 'x'.

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

Add '27' to each side of the equation.
-27 + 27 + x = 27.166155414 + 27

Combine like terms: -27 + 27 = 0
0 + x = 27.166155414 + 27
x = 27.166155414 + 27

Combine like terms: 27.166155414 + 27 = 54.166155414
x = 54.166155414

Simplifying
x = 54.166155414

Subproblem 2
x + -27 = -27.166155414

Simplifying
x + -27 = -27.166155414

Reorder the terms:
-27 + x = -27.166155414

Solving
-27 + x = -27.166155414

Solving for variable 'x'.

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

Add '27' to each side of the equation.
-27 + 27 + x = -27.166155414 + 27

Combine like terms: -27 + 27 = 0
0 + x = -27.166155414 + 27
x = -27.166155414 + 27

Combine like terms: -27.166155414 + 27 = -0.166155414
x = -0.166155414

Simplifying
x = -0.166155414

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {54.166155414, -0.166155414}