(10+2x)(5+2x)=54

Solution for (10+2x)(5+2x)=54 equation:

Simplifying
(10 + 2x)(5 + 2x) = 54

Multiply (10 + 2x) * (5 + 2x)
(10(5 + 2x) + 2x * (5 + 2x)) = 54
((5 * 10 + 2x * 10) + 2x * (5 + 2x)) = 54
((50 + 20x) + 2x * (5 + 2x)) = 54
(50 + 20x + (5 * 2x + 2x * 2x)) = 54
(50 + 20x + (10x + 4x2)) = 54

Combine like terms: 20x + 10x = 30x
(50 + 30x + 4x2) = 54

Solving
50 + 30x + 4x2 = 54

Solving for variable 'x'.

Reorder the terms:
50 + -54 + 30x + 4x2 = 54 + -54

Combine like terms: 50 + -54 = -4
-4 + 30x + 4x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-4 + 30x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 15x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
-2 + 15x + 2x2 = 0

Solving
-2 + 15x + 2x2 = 0

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

Divide each side by '2'.
-1 + 7.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 7.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 7.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 7.5x + x2 = 0 + 1
7.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
7.5x + x2 = 1

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 1 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 1 + 14.0625

Combine like terms: 1 + 14.0625 = 15.0625
14.0625 + 7.5x + x2 = 15.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 15.0625

Calculate the square root of the right side: 3.881043674

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.881043674 and -3.881043674.

Subproblem 1
x + 3.75 = 3.881043674

Simplifying
x + 3.75 = 3.881043674

Reorder the terms:
3.75 + x = 3.881043674

Solving
3.75 + x = 3.881043674

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 3.881043674 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.881043674 + -3.75
x = 3.881043674 + -3.75

Combine like terms: 3.881043674 + -3.75 = 0.131043674
x = 0.131043674

Simplifying
x = 0.131043674

Subproblem 2
x + 3.75 = -3.881043674

Simplifying
x + 3.75 = -3.881043674

Reorder the terms:
3.75 + x = -3.881043674

Solving
3.75 + x = -3.881043674

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -3.881043674 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.881043674 + -3.75
x = -3.881043674 + -3.75

Combine like terms: -3.881043674 + -3.75 = -7.631043674
x = -7.631043674

Simplifying
x = -7.631043674

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.131043674, -7.631043674}
Solution
x = {0.131043674, -7.631043674}