54=(2+x)(2x-5)

Solution for 54=(2+x)(2x-5) equation:

Simplifying
54 = (2 + x)(2x + -5)

Reorder the terms:
54 = (2 + x)(-5 + 2x)

Multiply (2 + x) * (-5 + 2x)
54 = (2(-5 + 2x) + x(-5 + 2x))
54 = ((-5 * 2 + 2x * 2) + x(-5 + 2x))
54 = ((-10 + 4x) + x(-5 + 2x))
54 = (-10 + 4x + (-5 * x + 2x * x))
54 = (-10 + 4x + (-5x + 2x2))

Combine like terms: 4x + -5x = -1x
54 = (-10 + -1x + 2x2)

Solving
54 = -10 + -1x + 2x2

Solving for variable 'x'.

Combine like terms: 54 + 10 = 64
64 + x + -2x2 = -10 + -1x + 2x2 + 10 + x + -2x2

Reorder the terms:
64 + x + -2x2 = -10 + 10 + -1x + x + 2x2 + -2x2

Combine like terms: -10 + 10 = 0
64 + x + -2x2 = 0 + -1x + x + 2x2 + -2x2
64 + x + -2x2 = -1x + x + 2x2 + -2x2

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

Combine like terms: 2x2 + -2x2 = 0
64 + x + -2x2 = 0

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

Divide each side by '-2'.
-32 + -0.5x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -0.5x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -0.5x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -0.5x + x2 = 0 + 32
-0.5x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-0.5x + x2 = 32

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.5x + 0.25 + x2 = 32 + 0.25

Reorder the terms:
0.25 + -0.5x + x2 = 32 + 0.25

Combine like terms: 32 + 0.25 = 32.25
0.25 + -0.5x + x2 = 32.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + 0.5 = 5.678908346

Simplifying
x + 0.5 = 5.678908346

Reorder the terms:
0.5 + x = 5.678908346

Solving
0.5 + x = 5.678908346

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.678908346 + -0.5
x = 5.678908346 + -0.5

Combine like terms: 5.678908346 + -0.5 = 5.178908346
x = 5.178908346

Simplifying
x = 5.178908346

Subproblem 2
x + 0.5 = -5.678908346

Simplifying
x + 0.5 = -5.678908346

Reorder the terms:
0.5 + x = -5.678908346

Solving
0.5 + x = -5.678908346

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.678908346 + -0.5
x = -5.678908346 + -0.5

Combine like terms: -5.678908346 + -0.5 = -6.178908346
x = -6.178908346

Simplifying
x = -6.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.178908346, -6.178908346}