(2.1x+3.2)(0.1x+0.4)=

Solution for (2.1x+3.2)(0.1x+0.4)= equation:

Simplifying
(2.1x + 3.2)(0.1x + 0.4) = 0

Reorder the terms:
(3.2 + 2.1x)(0.1x + 0.4) = 0

Reorder the terms:
(3.2 + 2.1x)(0.4 + 0.1x) = 0

Multiply (3.2 + 2.1x) * (0.4 + 0.1x)
(3.2(0.4 + 0.1x) + 2.1x * (0.4 + 0.1x)) = 0
((0.4 * 3.2 + 0.1x * 3.2) + 2.1x * (0.4 + 0.1x)) = 0
((1.28 + 0.32x) + 2.1x * (0.4 + 0.1x)) = 0
(1.28 + 0.32x + (0.4 * 2.1x + 0.1x * 2.1x)) = 0
(1.28 + 0.32x + (0.84x + 0.21x2)) = 0

Combine like terms: 0.32x + 0.84x = 1.16x
(1.28 + 1.16x + 0.21x2) = 0

Solving
1.28 + 1.16x + 0.21x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.21'.
6.095238095 + 5.523809524x + x2 = 0

Move the constant term to the right:

Add '-6.095238095' to each side of the equation.
6.095238095 + 5.523809524x + -6.095238095 + x2 = 0 + -6.095238095

Reorder the terms:
6.095238095 + -6.095238095 + 5.523809524x + x2 = 0 + -6.095238095

Combine like terms: 6.095238095 + -6.095238095 = 0.000000000
0.000000000 + 5.523809524x + x2 = 0 + -6.095238095
5.523809524x + x2 = 0 + -6.095238095

Combine like terms: 0 + -6.095238095 = -6.095238095
5.523809524x + x2 = -6.095238095

The x term is 5.523809524x.  Take half its coefficient (2.761904762).
Square it (7.628117914) and add it to both sides.

Add '7.628117914' to each side of the equation.
5.523809524x + 7.628117914 + x2 = -6.095238095 + 7.628117914

Reorder the terms:
7.628117914 + 5.523809524x + x2 = -6.095238095 + 7.628117914

Combine like terms: -6.095238095 + 7.628117914 = 1.532879819
7.628117914 + 5.523809524x + x2 = 1.532879819

Factor a perfect square on the left side:
(x + 2.761904762)(x + 2.761904762) = 1.532879819

Calculate the square root of the right side: 1.238095238

Break this problem into two subproblems by setting 
(x + 2.761904762) equal to 1.238095238 and -1.238095238.

Subproblem 1
x + 2.761904762 = 1.238095238

Simplifying
x + 2.761904762 = 1.238095238

Reorder the terms:
2.761904762 + x = 1.238095238

Solving
2.761904762 + x = 1.238095238

Solving for variable 'x'.

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

Add '-2.761904762' to each side of the equation.
2.761904762 + -2.761904762 + x = 1.238095238 + -2.761904762

Combine like terms: 2.761904762 + -2.761904762 = 0.000000000
0.000000000 + x = 1.238095238 + -2.761904762
x = 1.238095238 + -2.761904762

Combine like terms: 1.238095238 + -2.761904762 = -1.523809524
x = -1.523809524

Simplifying
x = -1.523809524

Subproblem 2
x + 2.761904762 = -1.238095238

Simplifying
x + 2.761904762 = -1.238095238

Reorder the terms:
2.761904762 + x = -1.238095238

Solving
2.761904762 + x = -1.238095238

Solving for variable 'x'.

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

Add '-2.761904762' to each side of the equation.
2.761904762 + -2.761904762 + x = -1.238095238 + -2.761904762

Combine like terms: 2.761904762 + -2.761904762 = 0.000000000
0.000000000 + x = -1.238095238 + -2.761904762
x = -1.238095238 + -2.761904762

Combine like terms: -1.238095238 + -2.761904762 = -4
x = -4

Simplifying
x = -4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.523809524, -4}