3(2x-3)-2x(x-5)=1

Solution for 3(2x-3)-2x(x-5)=1 equation:

Simplifying
3(2x + -3) + -2x(x + -5) = 1

Reorder the terms:
3(-3 + 2x) + -2x(x + -5) = 1
(-3 * 3 + 2x * 3) + -2x(x + -5) = 1
(-9 + 6x) + -2x(x + -5) = 1

Reorder the terms:
-9 + 6x + -2x(-5 + x) = 1
-9 + 6x + (-5 * -2x + x * -2x) = 1
-9 + 6x + (10x + -2x2) = 1

Combine like terms: 6x + 10x = 16x
-9 + 16x + -2x2 = 1

Solving
-9 + 16x + -2x2 = 1

Solving for variable 'x'.

Reorder the terms:
-9 + -1 + 16x + -2x2 = 1 + -1

Combine like terms: -9 + -1 = -10
-10 + 16x + -2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-10 + 16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 8x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
-5 + 8x + -1x2 = 0

Solving
-5 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -8x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -8x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x + x2 = 0 + -5
-8x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8x + x2 = -5

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -5 + 16

Reorder the terms:
16 + -8x + x2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8x + x2 = 11

Factor a perfect square on the left side:
(x + -4)(x + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -4) equal to 3.31662479 and -3.31662479.

Subproblem 1
x + -4 = 3.31662479

Simplifying
x + -4 = 3.31662479

Reorder the terms:
-4 + x = 3.31662479

Solving
-4 + x = 3.31662479

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.31662479 + 4
x = 3.31662479 + 4

Combine like terms: 3.31662479 + 4 = 7.31662479
x = 7.31662479

Simplifying
x = 7.31662479

Subproblem 2
x + -4 = -3.31662479

Simplifying
x + -4 = -3.31662479

Reorder the terms:
-4 + x = -3.31662479

Solving
-4 + x = -3.31662479

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.31662479 + 4
x = -3.31662479 + 4

Combine like terms: -3.31662479 + 4 = 0.68337521
x = 0.68337521

Simplifying
x = 0.68337521

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.31662479, 0.68337521}
Solution
x = {7.31662479, 0.68337521}