(21x-2)(38x+5)=180

Solution for (21x-2)(38x+5)=180 equation:

Simplifying
(21x + -2)(38x + 5) = 180

Reorder the terms:
(-2 + 21x)(38x + 5) = 180

Reorder the terms:
(-2 + 21x)(5 + 38x) = 180

Multiply (-2 + 21x) * (5 + 38x)
(-2(5 + 38x) + 21x * (5 + 38x)) = 180
((5 * -2 + 38x * -2) + 21x * (5 + 38x)) = 180
((-10 + -76x) + 21x * (5 + 38x)) = 180
(-10 + -76x + (5 * 21x + 38x * 21x)) = 180
(-10 + -76x + (105x + 798x2)) = 180

Combine like terms: -76x + 105x = 29x
(-10 + 29x + 798x2) = 180

Solving
-10 + 29x + 798x2 = 180

Solving for variable 'x'.

Reorder the terms:
-10 + -180 + 29x + 798x2 = 180 + -180

Combine like terms: -10 + -180 = -190
-190 + 29x + 798x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-190 + 29x + 798x2 = 0

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

Divide each side by '798'.
-0.2380952381 + 0.03634085213x + x2 = 0

Move the constant term to the right:

Add '0.2380952381' to each side of the equation.
-0.2380952381 + 0.03634085213x + 0.2380952381 + x2 = 0 + 0.2380952381

Reorder the terms:
-0.2380952381 + 0.2380952381 + 0.03634085213x + x2 = 0 + 0.2380952381

Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000
0.0000000000 + 0.03634085213x + x2 = 0 + 0.2380952381
0.03634085213x + x2 = 0 + 0.2380952381

Combine like terms: 0 + 0.2380952381 = 0.2380952381
0.03634085213x + x2 = 0.2380952381

The x term is 0.03634085213x.  Take half its coefficient (0.01817042607).
Square it (0.0003301643836) and add it to both sides.

Add '0.0003301643836' to each side of the equation.
0.03634085213x + 0.0003301643836 + x2 = 0.2380952381 + 0.0003301643836

Reorder the terms:
0.0003301643836 + 0.03634085213x + x2 = 0.2380952381 + 0.0003301643836

Combine like terms: 0.2380952381 + 0.0003301643836 = 0.2384254024836
0.0003301643836 + 0.03634085213x + x2 = 0.2384254024836

Factor a perfect square on the left side:
(x + 0.01817042607)(x + 0.01817042607) = 0.2384254024836

Calculate the square root of the right side: 0.488288237

Break this problem into two subproblems by setting 
(x + 0.01817042607) equal to 0.488288237 and -0.488288237.

Subproblem 1
x + 0.01817042607 = 0.488288237

Simplifying
x + 0.01817042607 = 0.488288237

Reorder the terms:
0.01817042607 + x = 0.488288237

Solving
0.01817042607 + x = 0.488288237

Solving for variable 'x'.

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

Add '-0.01817042607' to each side of the equation.
0.01817042607 + -0.01817042607 + x = 0.488288237 + -0.01817042607

Combine like terms: 0.01817042607 + -0.01817042607 = 0.00000000000
0.00000000000 + x = 0.488288237 + -0.01817042607
x = 0.488288237 + -0.01817042607

Combine like terms: 0.488288237 + -0.01817042607 = 0.47011781093
x = 0.47011781093

Simplifying
x = 0.47011781093

Subproblem 2
x + 0.01817042607 = -0.488288237

Simplifying
x + 0.01817042607 = -0.488288237

Reorder the terms:
0.01817042607 + x = -0.488288237

Solving
0.01817042607 + x = -0.488288237

Solving for variable 'x'.

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

Add '-0.01817042607' to each side of the equation.
0.01817042607 + -0.01817042607 + x = -0.488288237 + -0.01817042607

Combine like terms: 0.01817042607 + -0.01817042607 = 0.00000000000
0.00000000000 + x = -0.488288237 + -0.01817042607
x = -0.488288237 + -0.01817042607

Combine like terms: -0.488288237 + -0.01817042607 = -0.50645866307
x = -0.50645866307

Simplifying
x = -0.50645866307

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.47011781093, -0.50645866307}