(4.7x+8.6)(3.7x-1.4)=

Solution for (4.7x+8.6)(3.7x-1.4)= equation:

Simplifying
(4.7x + 8.6)(3.7x + -1.4) = 0

Reorder the terms:
(8.6 + 4.7x)(3.7x + -1.4) = 0

Reorder the terms:
(8.6 + 4.7x)(-1.4 + 3.7x) = 0

Multiply (8.6 + 4.7x) * (-1.4 + 3.7x)
(8.6(-1.4 + 3.7x) + 4.7x * (-1.4 + 3.7x)) = 0
((-1.4 * 8.6 + 3.7x * 8.6) + 4.7x * (-1.4 + 3.7x)) = 0
((-12.04 + 31.82x) + 4.7x * (-1.4 + 3.7x)) = 0
(-12.04 + 31.82x + (-1.4 * 4.7x + 3.7x * 4.7x)) = 0
(-12.04 + 31.82x + (-6.58x + 17.39x2)) = 0

Combine like terms: 31.82x + -6.58x = 25.24x
(-12.04 + 25.24x + 17.39x2) = 0

Solving
-12.04 + 25.24x + 17.39x2 = 0

Solving for variable 'x'.

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

Divide each side by '17.39'.
-0.6923519264 + 1.451408856x + x2 = 0

Move the constant term to the right:

Add '0.6923519264' to each side of the equation.
-0.6923519264 + 1.451408856x + 0.6923519264 + x2 = 0 + 0.6923519264

Reorder the terms:
-0.6923519264 + 0.6923519264 + 1.451408856x + x2 = 0 + 0.6923519264

Combine like terms: -0.6923519264 + 0.6923519264 = 0.0000000000
0.0000000000 + 1.451408856x + x2 = 0 + 0.6923519264
1.451408856x + x2 = 0 + 0.6923519264

Combine like terms: 0 + 0.6923519264 = 0.6923519264
1.451408856x + x2 = 0.6923519264

The x term is 1.451408856x.  Take half its coefficient (0.725704428).
Square it (0.5266469168) and add it to both sides.

Add '0.5266469168' to each side of the equation.
1.451408856x + 0.5266469168 + x2 = 0.6923519264 + 0.5266469168

Reorder the terms:
0.5266469168 + 1.451408856x + x2 = 0.6923519264 + 0.5266469168

Combine like terms: 0.6923519264 + 0.5266469168 = 1.2189988432
0.5266469168 + 1.451408856x + x2 = 1.2189988432

Factor a perfect square on the left side:
(x + 0.725704428)(x + 0.725704428) = 1.2189988432

Calculate the square root of the right side: 1.104082806

Break this problem into two subproblems by setting 
(x + 0.725704428) equal to 1.104082806 and -1.104082806.

Subproblem 1
x + 0.725704428 = 1.104082806

Simplifying
x + 0.725704428 = 1.104082806

Reorder the terms:
0.725704428 + x = 1.104082806

Solving
0.725704428 + x = 1.104082806

Solving for variable 'x'.

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

Add '-0.725704428' to each side of the equation.
0.725704428 + -0.725704428 + x = 1.104082806 + -0.725704428

Combine like terms: 0.725704428 + -0.725704428 = 0.000000000
0.000000000 + x = 1.104082806 + -0.725704428
x = 1.104082806 + -0.725704428

Combine like terms: 1.104082806 + -0.725704428 = 0.378378378
x = 0.378378378

Simplifying
x = 0.378378378

Subproblem 2
x + 0.725704428 = -1.104082806

Simplifying
x + 0.725704428 = -1.104082806

Reorder the terms:
0.725704428 + x = -1.104082806

Solving
0.725704428 + x = -1.104082806

Solving for variable 'x'.

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

Add '-0.725704428' to each side of the equation.
0.725704428 + -0.725704428 + x = -1.104082806 + -0.725704428

Combine like terms: 0.725704428 + -0.725704428 = 0.000000000
0.000000000 + x = -1.104082806 + -0.725704428
x = -1.104082806 + -0.725704428

Combine like terms: -1.104082806 + -0.725704428 = -1.829787234
x = -1.829787234

Simplifying
x = -1.829787234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.378378378, -1.829787234}