5x+3(-4x*4x+6)-3x+1=17

Solution for 5x+3(-4x*4x+6)-3x+1=17 equation:

Simplifying
5x + 3(-4x * 4x + 6) + -3x + 1 = 17

Reorder the terms for easier multiplication:
5x + 3(-4 * 4x * x + 6) + -3x + 1 = 17

Multiply -4 * 4
5x + 3(-16x * x + 6) + -3x + 1 = 17

Multiply x * x
5x + 3(-16x2 + 6) + -3x + 1 = 17

Reorder the terms:
5x + 3(6 + -16x2) + -3x + 1 = 17
5x + (6 * 3 + -16x2 * 3) + -3x + 1 = 17
5x + (18 + -48x2) + -3x + 1 = 17

Reorder the terms:
18 + 1 + 5x + -3x + -48x2 = 17

Combine like terms: 18 + 1 = 19
19 + 5x + -3x + -48x2 = 17

Combine like terms: 5x + -3x = 2x
19 + 2x + -48x2 = 17

Solving
19 + 2x + -48x2 = 17

Solving for variable 'x'.

Reorder the terms:
19 + -17 + 2x + -48x2 = 17 + -17

Combine like terms: 19 + -17 = 2
2 + 2x + -48x2 = 17 + -17

Combine like terms: 17 + -17 = 0
2 + 2x + -48x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + x + -24x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + x + -24x2)' equal to zero and attempt to solve:

Simplifying
1 + x + -24x2 = 0

Solving
1 + x + -24x2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
-0.04166666667 + -0.04166666667x + x2 = 0

Move the constant term to the right:

Add '0.04166666667' to each side of the equation.
-0.04166666667 + -0.04166666667x + 0.04166666667 + x2 = 0 + 0.04166666667

Reorder the terms:
-0.04166666667 + 0.04166666667 + -0.04166666667x + x2 = 0 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + -0.04166666667x + x2 = 0 + 0.04166666667
-0.04166666667x + x2 = 0 + 0.04166666667

Combine like terms: 0 + 0.04166666667 = 0.04166666667
-0.04166666667x + x2 = 0.04166666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.04166666667x + 0.25 + x2 = 0.04166666667 + 0.25

Reorder the terms:
0.25 + -0.04166666667x + x2 = 0.04166666667 + 0.25

Combine like terms: 0.04166666667 + 0.25 = 0.29166666667
0.25 + -0.04166666667x + x2 = 0.29166666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.29166666667

Calculate the square root of the right side: 0.540061725

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.540061725 and -0.540061725.

Subproblem 1
x + 0.5 = 0.540061725

Simplifying
x + 0.5 = 0.540061725

Reorder the terms:
0.5 + x = 0.540061725

Solving
0.5 + x = 0.540061725

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.540061725 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.540061725 + -0.5
x = 0.540061725 + -0.5

Combine like terms: 0.540061725 + -0.5 = 0.040061725
x = 0.040061725

Simplifying
x = 0.040061725

Subproblem 2
x + 0.5 = -0.540061725

Simplifying
x + 0.5 = -0.540061725

Reorder the terms:
0.5 + x = -0.540061725

Solving
0.5 + x = -0.540061725

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.540061725 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.540061725 + -0.5
x = -0.540061725 + -0.5

Combine like terms: -0.540061725 + -0.5 = -1.040061725
x = -1.040061725

Simplifying
x = -1.040061725

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.040061725, -1.040061725}
Solution
x = {0.040061725, -1.040061725}