(3x-1)(5x+4)-15x*15x=17

Solution for (3x-1)(5x+4)-15x*15x=17 equation:

Simplifying
(3x + -1)(5x + 4) + -15x * 15x = 17

Reorder the terms:
(-1 + 3x)(5x + 4) + -15x * 15x = 17

Reorder the terms:
(-1 + 3x)(4 + 5x) + -15x * 15x = 17

Multiply (-1 + 3x) * (4 + 5x)
(-1(4 + 5x) + 3x * (4 + 5x)) + -15x * 15x = 17
((4 * -1 + 5x * -1) + 3x * (4 + 5x)) + -15x * 15x = 17
((-4 + -5x) + 3x * (4 + 5x)) + -15x * 15x = 17
(-4 + -5x + (4 * 3x + 5x * 3x)) + -15x * 15x = 17
(-4 + -5x + (12x + 15x2)) + -15x * 15x = 17

Combine like terms: -5x + 12x = 7x
(-4 + 7x + 15x2) + -15x * 15x = 17

Reorder the terms for easier multiplication:
-4 + 7x + 15x2 + -15 * 15x * x = 17

Multiply -15 * 15
-4 + 7x + 15x2 + -225x * x = 17

Multiply x * x
-4 + 7x + 15x2 + -225x2 = 17

Combine like terms: 15x2 + -225x2 = -210x2
-4 + 7x + -210x2 = 17

Solving
-4 + 7x + -210x2 = 17

Solving for variable 'x'.

Reorder the terms:
-4 + -17 + 7x + -210x2 = 17 + -17

Combine like terms: -4 + -17 = -21
-21 + 7x + -210x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-21 + 7x + -210x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + x + -30x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-3 + x + -30x2)' equal to zero and attempt to solve:

Simplifying
-3 + x + -30x2 = 0

Solving
-3 + x + -30x2 = 0

Begin completing the square.  Divide all terms by
-30 the coefficient of the squared term: 

Divide each side by '-30'.
0.1 + -0.03333333333x + x2 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -0.03333333333x + -0.1 + x2 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + -0.03333333333x + x2 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -0.03333333333x + x2 = 0.0 + -0.1
-0.03333333333x + x2 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
-0.03333333333x + x2 = -0.1

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.
-0.03333333333x + 0.25 + x2 = -0.1 + 0.25

Reorder the terms:
0.25 + -0.03333333333x + x2 = -0.1 + 0.25

Combine like terms: -0.1 + 0.25 = 0.15
0.25 + -0.03333333333x + x2 = 0.15

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.15

Calculate the square root of the right side: 0.387298335

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.387298335 and -0.387298335.

Subproblem 1
x + 0.5 = 0.387298335

Simplifying
x + 0.5 = 0.387298335

Reorder the terms:
0.5 + x = 0.387298335

Solving
0.5 + x = 0.387298335

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 = 0.387298335 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.387298335 + -0.5
x = 0.387298335 + -0.5

Combine like terms: 0.387298335 + -0.5 = -0.112701665
x = -0.112701665

Simplifying
x = -0.112701665

Subproblem 2
x + 0.5 = -0.387298335

Simplifying
x + 0.5 = -0.387298335

Reorder the terms:
0.5 + x = -0.387298335

Solving
0.5 + x = -0.387298335

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 = -0.387298335 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.387298335 + -0.5
x = -0.387298335 + -0.5

Combine like terms: -0.387298335 + -0.5 = -0.887298335
x = -0.887298335

Simplifying
x = -0.887298335

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.112701665, -0.887298335}
Solution
x = {-0.112701665, -0.887298335}