(26+2x)(10+2x)=832

Solution for (26+2x)(10+2x)=832 equation:

Simplifying
(26 + 2x)(10 + 2x) = 832

Multiply (26 + 2x) * (10 + 2x)
(26(10 + 2x) + 2x * (10 + 2x)) = 832
((10 * 26 + 2x * 26) + 2x * (10 + 2x)) = 832
((260 + 52x) + 2x * (10 + 2x)) = 832
(260 + 52x + (10 * 2x + 2x * 2x)) = 832
(260 + 52x + (20x + 4x2)) = 832

Combine like terms: 52x + 20x = 72x
(260 + 72x + 4x2) = 832

Solving
260 + 72x + 4x2 = 832

Solving for variable 'x'.

Reorder the terms:
260 + -832 + 72x + 4x2 = 832 + -832

Combine like terms: 260 + -832 = -572
-572 + 72x + 4x2 = 832 + -832

Combine like terms: 832 + -832 = 0
-572 + 72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-143 + 18x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-143 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
-143 + 18x + x2 = 0

Solving
-143 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '143' to each side of the equation.
-143 + 18x + 143 + x2 = 0 + 143

Reorder the terms:
-143 + 143 + 18x + x2 = 0 + 143

Combine like terms: -143 + 143 = 0
0 + 18x + x2 = 0 + 143
18x + x2 = 0 + 143

Combine like terms: 0 + 143 = 143
18x + x2 = 143

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = 143 + 81

Reorder the terms:
81 + 18x + x2 = 143 + 81

Combine like terms: 143 + 81 = 224
81 + 18x + x2 = 224

Factor a perfect square on the left side:
(x + 9)(x + 9) = 224

Calculate the square root of the right side: 14.966629547

Break this problem into two subproblems by setting 
(x + 9) equal to 14.966629547 and -14.966629547.

Subproblem 1
x + 9 = 14.966629547

Simplifying
x + 9 = 14.966629547

Reorder the terms:
9 + x = 14.966629547

Solving
9 + x = 14.966629547

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 14.966629547 + -9

Combine like terms: 9 + -9 = 0
0 + x = 14.966629547 + -9
x = 14.966629547 + -9

Combine like terms: 14.966629547 + -9 = 5.966629547
x = 5.966629547

Simplifying
x = 5.966629547

Subproblem 2
x + 9 = -14.966629547

Simplifying
x + 9 = -14.966629547

Reorder the terms:
9 + x = -14.966629547

Solving
9 + x = -14.966629547

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -14.966629547 + -9

Combine like terms: 9 + -9 = 0
0 + x = -14.966629547 + -9
x = -14.966629547 + -9

Combine like terms: -14.966629547 + -9 = -23.966629547
x = -23.966629547

Simplifying
x = -23.966629547

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.966629547, -23.966629547}
Solution
x = {5.966629547, -23.966629547}