(7x+1)(18x+4)=50

Solution for (7x+1)(18x+4)=50 equation:

Simplifying
(7x + 1)(18x + 4) = 50

Reorder the terms:
(1 + 7x)(18x + 4) = 50

Reorder the terms:
(1 + 7x)(4 + 18x) = 50

Multiply (1 + 7x) * (4 + 18x)
(1(4 + 18x) + 7x * (4 + 18x)) = 50
((4 * 1 + 18x * 1) + 7x * (4 + 18x)) = 50
((4 + 18x) + 7x * (4 + 18x)) = 50
(4 + 18x + (4 * 7x + 18x * 7x)) = 50
(4 + 18x + (28x + 126x2)) = 50

Combine like terms: 18x + 28x = 46x
(4 + 46x + 126x2) = 50

Solving
4 + 46x + 126x2 = 50

Solving for variable 'x'.

Reorder the terms:
4 + -50 + 46x + 126x2 = 50 + -50

Combine like terms: 4 + -50 = -46
-46 + 46x + 126x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-46 + 46x + 126x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-23 + 23x + 63x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-23 + 23x + 63x2)' equal to zero and attempt to solve:

Simplifying
-23 + 23x + 63x2 = 0

Solving
-23 + 23x + 63x2 = 0

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

Divide each side by '63'.
-0.3650793651 + 0.3650793651x + x2 = 0

Move the constant term to the right:

Add '0.3650793651' to each side of the equation.
-0.3650793651 + 0.3650793651x + 0.3650793651 + x2 = 0 + 0.3650793651

Reorder the terms:
-0.3650793651 + 0.3650793651 + 0.3650793651x + x2 = 0 + 0.3650793651

Combine like terms: -0.3650793651 + 0.3650793651 = 0.0000000000
0.0000000000 + 0.3650793651x + x2 = 0 + 0.3650793651
0.3650793651x + x2 = 0 + 0.3650793651

Combine like terms: 0 + 0.3650793651 = 0.3650793651
0.3650793651x + x2 = 0.3650793651

The x term is 0.3650793651x.  Take half its coefficient (0.1825396826).
Square it (0.03332073572) and add it to both sides.

Add '0.03332073572' to each side of the equation.
0.3650793651x + 0.03332073572 + x2 = 0.3650793651 + 0.03332073572

Reorder the terms:
0.03332073572 + 0.3650793651x + x2 = 0.3650793651 + 0.03332073572

Combine like terms: 0.3650793651 + 0.03332073572 = 0.39840010082
0.03332073572 + 0.3650793651x + x2 = 0.39840010082

Factor a perfect square on the left side:
(x + 0.1825396826)(x + 0.1825396826) = 0.39840010082

Calculate the square root of the right side: 0.631189433

Break this problem into two subproblems by setting 
(x + 0.1825396826) equal to 0.631189433 and -0.631189433.

Subproblem 1
x + 0.1825396826 = 0.631189433

Simplifying
x + 0.1825396826 = 0.631189433

Reorder the terms:
0.1825396826 + x = 0.631189433

Solving
0.1825396826 + x = 0.631189433

Solving for variable 'x'.

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

Add '-0.1825396826' to each side of the equation.
0.1825396826 + -0.1825396826 + x = 0.631189433 + -0.1825396826

Combine like terms: 0.1825396826 + -0.1825396826 = 0.0000000000
0.0000000000 + x = 0.631189433 + -0.1825396826
x = 0.631189433 + -0.1825396826

Combine like terms: 0.631189433 + -0.1825396826 = 0.4486497504
x = 0.4486497504

Simplifying
x = 0.4486497504

Subproblem 2
x + 0.1825396826 = -0.631189433

Simplifying
x + 0.1825396826 = -0.631189433

Reorder the terms:
0.1825396826 + x = -0.631189433

Solving
0.1825396826 + x = -0.631189433

Solving for variable 'x'.

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

Add '-0.1825396826' to each side of the equation.
0.1825396826 + -0.1825396826 + x = -0.631189433 + -0.1825396826

Combine like terms: 0.1825396826 + -0.1825396826 = 0.0000000000
0.0000000000 + x = -0.631189433 + -0.1825396826
x = -0.631189433 + -0.1825396826

Combine like terms: -0.631189433 + -0.1825396826 = -0.8137291156
x = -0.8137291156

Simplifying
x = -0.8137291156

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4486497504, -0.8137291156}
Solution
x = {0.4486497504, -0.8137291156}