(10+2x)(5+2x)=75

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Solution for (10+2x)(5+2x)=75 equation: 


Simplifying
(10 + 2x)(5 + 2x) = 75

Multiply (10 + 2x) * (5 + 2x)
(10(5 + 2x) + 2x * (5 + 2x)) = 75
((5 * 10 + 2x * 10) + 2x * (5 + 2x)) = 75
((50 + 20x) + 2x * (5 + 2x)) = 75
(50 + 20x + (5 * 2x + 2x * 2x)) = 75
(50 + 20x + (10x + 4x2)) = 75

Combine like terms: 20x + 10x = 30x
(50 + 30x + 4x2) = 75

Solving
50 + 30x + 4x2 = 75

Solving for variable 'x'.

Reorder the terms:
50 + -75 + 30x + 4x2 = 75 + -75

Combine like terms: 50 + -75 = -25
-25 + 30x + 4x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-25 + 30x + 4x2 = 0

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

Divide each side by '4'.
-6.25 + 7.5x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 7.5x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 7.5x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 7.5x + x2 = 0 + 6.25
7.5x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
7.5x + x2 = 6.25

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 = 6.25 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 6.25 + 14.0625

Combine like terms: 6.25 + 14.0625 = 20.3125
14.0625 + 7.5x + x2 = 20.3125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 20.3125

Calculate the square root of the right side: 4.506939094

Break this problem into two subproblems by setting 
(x + 3.75) equal to 4.506939094 and -4.506939094.


Subproblem 1
x + 3.75 = 4.506939094

Simplifying
x + 3.75 = 4.506939094

Reorder the terms:
3.75 + x = 4.506939094

Solving
3.75 + x = 4.506939094

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 = 4.506939094 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 4.506939094 + -3.75
x = 4.506939094 + -3.75

Combine like terms: 4.506939094 + -3.75 = 0.756939094
x = 0.756939094

Simplifying
x = 0.756939094


Subproblem 2
x + 3.75 = -4.506939094

Simplifying
x + 3.75 = -4.506939094

Reorder the terms:
3.75 + x = -4.506939094

Solving
3.75 + x = -4.506939094

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 = -4.506939094 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -4.506939094 + -3.75
x = -4.506939094 + -3.75

Combine like terms: -4.506939094 + -3.75 = -8.256939094
x = -8.256939094

Simplifying
x = -8.256939094


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.756939094, -8.256939094}

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