-3x-3x(5x-17)=3

Solution for -3x-3x(5x-17)=3 equation:

Simplifying
-3x + -3x(5x + -17) = 3

Reorder the terms:
-3x + -3x(-17 + 5x) = 3
-3x + (-17 * -3x + 5x * -3x) = 3
-3x + (51x + -15x2) = 3

Combine like terms: -3x + 51x = 48x
48x + -15x2 = 3

Solving
48x + -15x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 48x + -15x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 48x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 16x + -5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 16x + -5x2)' equal to zero and attempt to solve:

Simplifying
-1 + 16x + -5x2 = 0

Solving
-1 + 16x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.2 + -3.2x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -3.2x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -3.2x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -3.2x + x2 = 0 + -0.2
-3.2x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-3.2x + x2 = -0.2

The x term is -3.2x.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2x + 2.56 + x2 = -0.2 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = -0.2 + 2.56

Combine like terms: -0.2 + 2.56 = 2.36
2.56 + -3.2x + x2 = 2.36

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 2.36

Calculate the square root of the right side: 1.53622915

Break this problem into two subproblems by setting 
(x + -1.6) equal to 1.53622915 and -1.53622915.

Subproblem 1
x + -1.6 = 1.53622915

Simplifying
x + -1.6 = 1.53622915

Reorder the terms:
-1.6 + x = 1.53622915

Solving
-1.6 + x = 1.53622915

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = 1.53622915 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = 1.53622915 + 1.6
x = 1.53622915 + 1.6

Combine like terms: 1.53622915 + 1.6 = 3.13622915
x = 3.13622915

Simplifying
x = 3.13622915

Subproblem 2
x + -1.6 = -1.53622915

Simplifying
x + -1.6 = -1.53622915

Reorder the terms:
-1.6 + x = -1.53622915

Solving
-1.6 + x = -1.53622915

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = -1.53622915 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = -1.53622915 + 1.6
x = -1.53622915 + 1.6

Combine like terms: -1.53622915 + 1.6 = 0.06377085
x = 0.06377085

Simplifying
x = 0.06377085

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.13622915, 0.06377085}
Solution
x = {3.13622915, 0.06377085}