(30+2x)(50+2x)=1674

Solution for (30+2x)(50+2x)=1674 equation:

Simplifying
(30 + 2x)(50 + 2x) = 1674

Multiply (30 + 2x) * (50 + 2x)
(30(50 + 2x) + 2x * (50 + 2x)) = 1674
((50 * 30 + 2x * 30) + 2x * (50 + 2x)) = 1674
((1500 + 60x) + 2x * (50 + 2x)) = 1674
(1500 + 60x + (50 * 2x + 2x * 2x)) = 1674
(1500 + 60x + (100x + 4x2)) = 1674

Combine like terms: 60x + 100x = 160x
(1500 + 160x + 4x2) = 1674

Solving
1500 + 160x + 4x2 = 1674

Solving for variable 'x'.

Reorder the terms:
1500 + -1674 + 160x + 4x2 = 1674 + -1674

Combine like terms: 1500 + -1674 = -174
-174 + 160x + 4x2 = 1674 + -1674

Combine like terms: 1674 + -1674 = 0
-174 + 160x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-87 + 80x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-87 + 80x + 2x2)' equal to zero and attempt to solve:

Simplifying
-87 + 80x + 2x2 = 0

Solving
-87 + 80x + 2x2 = 0

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

Divide each side by '2'.
-43.5 + 40x + x2 = 0

Move the constant term to the right:

Add '43.5' to each side of the equation.
-43.5 + 40x + 43.5 + x2 = 0 + 43.5

Reorder the terms:
-43.5 + 43.5 + 40x + x2 = 0 + 43.5

Combine like terms: -43.5 + 43.5 = 0.0
0.0 + 40x + x2 = 0 + 43.5
40x + x2 = 0 + 43.5

Combine like terms: 0 + 43.5 = 43.5
40x + x2 = 43.5

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = 43.5 + 400

Reorder the terms:
400 + 40x + x2 = 43.5 + 400

Combine like terms: 43.5 + 400 = 443.5
400 + 40x + x2 = 443.5

Factor a perfect square on the left side:
(x + 20)(x + 20) = 443.5

Calculate the square root of the right side: 21.059439689

Break this problem into two subproblems by setting 
(x + 20) equal to 21.059439689 and -21.059439689.

Subproblem 1
x + 20 = 21.059439689

Simplifying
x + 20 = 21.059439689

Reorder the terms:
20 + x = 21.059439689

Solving
20 + x = 21.059439689

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = 21.059439689 + -20

Combine like terms: 20 + -20 = 0
0 + x = 21.059439689 + -20
x = 21.059439689 + -20

Combine like terms: 21.059439689 + -20 = 1.059439689
x = 1.059439689

Simplifying
x = 1.059439689

Subproblem 2
x + 20 = -21.059439689

Simplifying
x + 20 = -21.059439689

Reorder the terms:
20 + x = -21.059439689

Solving
20 + x = -21.059439689

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = -21.059439689 + -20

Combine like terms: 20 + -20 = 0
0 + x = -21.059439689 + -20
x = -21.059439689 + -20

Combine like terms: -21.059439689 + -20 = -41.059439689
x = -41.059439689

Simplifying
x = -41.059439689

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.059439689, -41.059439689}
Solution
x = {1.059439689, -41.059439689}