-17.1(x-3.4)(x+5.6)=0

Solution for -17.1(x-3.4)(x+5.6)=0 equation:

Simplifying
-17.1(x + -3.4)(x + 5.6) = 0

Reorder the terms:
-17.1(-3.4 + x)(x + 5.6) = 0

Reorder the terms:
-17.1(-3.4 + x)(5.6 + x) = 0

Multiply (-3.4 + x) * (5.6 + x)
-17.1(-3.4(5.6 + x) + x(5.6 + x)) = 0
-17.1((5.6 * -3.4 + x * -3.4) + x(5.6 + x)) = 0
-17.1((-19.04 + -3.4x) + x(5.6 + x)) = 0
-17.1(-19.04 + -3.4x + (5.6 * x + x * x)) = 0
-17.1(-19.04 + -3.4x + (5.6x + x2)) = 0

Combine like terms: -3.4x + 5.6x = 2.2x
-17.1(-19.04 + 2.2x + x2) = 0
(-19.04 * -17.1 + 2.2x * -17.1 + x2 * -17.1) = 0
(325.584 + -37.62x + -17.1x2) = 0

Solving
325.584 + -37.62x + -17.1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-17.1 the coefficient of the squared term: 

Divide each side by '-17.1'.
-19.04 + 2.2x + x2 = 0

Move the constant term to the right:

Add '19.04' to each side of the equation.
-19.04 + 2.2x + 19.04 + x2 = 0 + 19.04

Reorder the terms:
-19.04 + 19.04 + 2.2x + x2 = 0 + 19.04

Combine like terms: -19.04 + 19.04 = 0.00
0.00 + 2.2x + x2 = 0 + 19.04
2.2x + x2 = 0 + 19.04

Combine like terms: 0 + 19.04 = 19.04
2.2x + x2 = 19.04

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = 19.04 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = 19.04 + 1.21

Combine like terms: 19.04 + 1.21 = 20.25
1.21 + 2.2x + x2 = 20.25

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 20.25

Calculate the square root of the right side: 4.5

Break this problem into two subproblems by setting 
(x + 1.1) equal to 4.5 and -4.5.

Subproblem 1
x + 1.1 = 4.5

Simplifying
x + 1.1 = 4.5

Reorder the terms:
1.1 + x = 4.5

Solving
1.1 + x = 4.5

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = 4.5 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = 4.5 + -1.1
x = 4.5 + -1.1

Combine like terms: 4.5 + -1.1 = 3.4
x = 3.4

Simplifying
x = 3.4

Subproblem 2
x + 1.1 = -4.5

Simplifying
x + 1.1 = -4.5

Reorder the terms:
1.1 + x = -4.5

Solving
1.1 + x = -4.5

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = -4.5 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = -4.5 + -1.1
x = -4.5 + -1.1

Combine like terms: -4.5 + -1.1 = -5.6
x = -5.6

Simplifying
x = -5.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.4, -5.6}