3.2(x-4)+2x^2+1.7(x-3)=27

Solution for 3.2(x-4)+2x^2+1.7(x-3)=27 equation:

Simplifying
3.2(x + -4) + 2x2 + 1.7(x + -3) = 27

Reorder the terms:
3.2(-4 + x) + 2x2 + 1.7(x + -3) = 27
(-4 * 3.2 + x * 3.2) + 2x2 + 1.7(x + -3) = 27
(-12.8 + 3.2x) + 2x2 + 1.7(x + -3) = 27

Reorder the terms:
-12.8 + 3.2x + 2x2 + 1.7(-3 + x) = 27
-12.8 + 3.2x + 2x2 + (-3 * 1.7 + x * 1.7) = 27
-12.8 + 3.2x + 2x2 + (-5.1 + 1.7x) = 27

Reorder the terms:
-12.8 + -5.1 + 3.2x + 1.7x + 2x2 = 27

Combine like terms: -12.8 + -5.1 = -17.9
-17.9 + 3.2x + 1.7x + 2x2 = 27

Combine like terms: 3.2x + 1.7x = 4.9x
-17.9 + 4.9x + 2x2 = 27

Solving
-17.9 + 4.9x + 2x2 = 27

Solving for variable 'x'.

Reorder the terms:
-17.9 + -27 + 4.9x + 2x2 = 27 + -27

Combine like terms: -17.9 + -27 = -44.9
-44.9 + 4.9x + 2x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-44.9 + 4.9x + 2x2 = 0

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

Divide each side by '2'.
-22.45 + 2.45x + x2 = 0

Move the constant term to the right:

Add '22.45' to each side of the equation.
-22.45 + 2.45x + 22.45 + x2 = 0 + 22.45

Reorder the terms:
-22.45 + 22.45 + 2.45x + x2 = 0 + 22.45

Combine like terms: -22.45 + 22.45 = 0.00
0.00 + 2.45x + x2 = 0 + 22.45
2.45x + x2 = 0 + 22.45

Combine like terms: 0 + 22.45 = 22.45
2.45x + x2 = 22.45

The x term is 2.45x.  Take half its coefficient (1.225).
Square it (1.500625) and add it to both sides.

Add '1.500625' to each side of the equation.
2.45x + 1.500625 + x2 = 22.45 + 1.500625

Reorder the terms:
1.500625 + 2.45x + x2 = 22.45 + 1.500625

Combine like terms: 22.45 + 1.500625 = 23.950625
1.500625 + 2.45x + x2 = 23.950625

Factor a perfect square on the left side:
(x + 1.225)(x + 1.225) = 23.950625

Calculate the square root of the right side: 4.893937576

Break this problem into two subproblems by setting 
(x + 1.225) equal to 4.893937576 and -4.893937576.

Subproblem 1
x + 1.225 = 4.893937576

Simplifying
x + 1.225 = 4.893937576

Reorder the terms:
1.225 + x = 4.893937576

Solving
1.225 + x = 4.893937576

Solving for variable 'x'.

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

Add '-1.225' to each side of the equation.
1.225 + -1.225 + x = 4.893937576 + -1.225

Combine like terms: 1.225 + -1.225 = 0.000
0.000 + x = 4.893937576 + -1.225
x = 4.893937576 + -1.225

Combine like terms: 4.893937576 + -1.225 = 3.668937576
x = 3.668937576

Simplifying
x = 3.668937576

Subproblem 2
x + 1.225 = -4.893937576

Simplifying
x + 1.225 = -4.893937576

Reorder the terms:
1.225 + x = -4.893937576

Solving
1.225 + x = -4.893937576

Solving for variable 'x'.

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

Add '-1.225' to each side of the equation.
1.225 + -1.225 + x = -4.893937576 + -1.225

Combine like terms: 1.225 + -1.225 = 0.000
0.000 + x = -4.893937576 + -1.225
x = -4.893937576 + -1.225

Combine like terms: -4.893937576 + -1.225 = -6.118937576
x = -6.118937576

Simplifying
x = -6.118937576

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.668937576, -6.118937576}