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

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

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

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

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

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

Combine like terms: -5x + 2x = -3x
2(-10 + -3x + x2) = 54
(-10 * 2 + -3x * 2 + x2 * 2) = 54
(-20 + -6x + 2x2) = 54

Solving
-20 + -6x + 2x2 = 54

Solving for variable 'x'.

Reorder the terms:
-20 + -54 + -6x + 2x2 = 54 + -54

Combine like terms: -20 + -54 = -74
-74 + -6x + 2x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-74 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-37 + -3x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-37 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-37 + -3x + x2 = 0

Solving
-37 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -3x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + -3x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -3x + x2 = 0 + 37
-3x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
-3x + x2 = 37

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 37 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 37 + 2.25

Combine like terms: 37 + 2.25 = 39.25
2.25 + -3x + x2 = 39.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + -1.5) equal to 6.264982043 and -6.264982043.

Subproblem 1
x + -1.5 = 6.264982043

Simplifying
x + -1.5 = 6.264982043

Reorder the terms:
-1.5 + x = 6.264982043

Solving
-1.5 + x = 6.264982043

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 6.264982043 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 6.264982043 + 1.5
x = 6.264982043 + 1.5

Combine like terms: 6.264982043 + 1.5 = 7.764982043
x = 7.764982043

Simplifying
x = 7.764982043

Subproblem 2
x + -1.5 = -6.264982043

Simplifying
x + -1.5 = -6.264982043

Reorder the terms:
-1.5 + x = -6.264982043

Solving
-1.5 + x = -6.264982043

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -6.264982043 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -6.264982043 + 1.5
x = -6.264982043 + 1.5

Combine like terms: -6.264982043 + 1.5 = -4.764982043
x = -4.764982043

Simplifying
x = -4.764982043

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.764982043, -4.764982043}
Solution
x = {7.764982043, -4.764982043}