-3x+6-5(x-1)=-5x(2x-4)+5

Solution for -3x+6-5(x-1)=-5x(2x-4)+5 equation:

Simplifying
-3x + 6 + -5(x + -1) = -5x(2x + -4) + 5

Reorder the terms:
-3x + 6 + -5(-1 + x) = -5x(2x + -4) + 5
-3x + 6 + (-1 * -5 + x * -5) = -5x(2x + -4) + 5
-3x + 6 + (5 + -5x) = -5x(2x + -4) + 5

Reorder the terms:
6 + 5 + -3x + -5x = -5x(2x + -4) + 5

Combine like terms: 6 + 5 = 11
11 + -3x + -5x = -5x(2x + -4) + 5

Combine like terms: -3x + -5x = -8x
11 + -8x = -5x(2x + -4) + 5

Reorder the terms:
11 + -8x = -5x(-4 + 2x) + 5
11 + -8x = (-4 * -5x + 2x * -5x) + 5
11 + -8x = (20x + -10x2) + 5

Reorder the terms:
11 + -8x = 5 + 20x + -10x2

Solving
11 + -8x = 5 + 20x + -10x2

Solving for variable 'x'.

Reorder the terms:
11 + -5 + -8x + -20x + 10x2 = 5 + 20x + -10x2 + -5 + -20x + 10x2

Combine like terms: 11 + -5 = 6
6 + -8x + -20x + 10x2 = 5 + 20x + -10x2 + -5 + -20x + 10x2

Combine like terms: -8x + -20x = -28x
6 + -28x + 10x2 = 5 + 20x + -10x2 + -5 + -20x + 10x2

Reorder the terms:
6 + -28x + 10x2 = 5 + -5 + 20x + -20x + -10x2 + 10x2

Combine like terms: 5 + -5 = 0
6 + -28x + 10x2 = 0 + 20x + -20x + -10x2 + 10x2
6 + -28x + 10x2 = 20x + -20x + -10x2 + 10x2

Combine like terms: 20x + -20x = 0
6 + -28x + 10x2 = 0 + -10x2 + 10x2
6 + -28x + 10x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
6 + -28x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -14x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -14x + 5x2)' equal to zero and attempt to solve:

Simplifying
3 + -14x + 5x2 = 0

Solving
3 + -14x + 5x2 = 0

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

Divide each side by '5'.
0.6 + -2.8x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -2.8x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -2.8x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -2.8x + x2 = 0 + -0.6
-2.8x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-2.8x + x2 = -0.6

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = -0.6 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = -0.6 + 1.96

Combine like terms: -0.6 + 1.96 = 1.36
1.96 + -2.8x + x2 = 1.36

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 1.36

Calculate the square root of the right side: 1.166190379

Break this problem into two subproblems by setting 
(x + -1.4) equal to 1.166190379 and -1.166190379.

Subproblem 1
x + -1.4 = 1.166190379

Simplifying
x + -1.4 = 1.166190379

Reorder the terms:
-1.4 + x = 1.166190379

Solving
-1.4 + x = 1.166190379

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = 1.166190379 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = 1.166190379 + 1.4
x = 1.166190379 + 1.4

Combine like terms: 1.166190379 + 1.4 = 2.566190379
x = 2.566190379

Simplifying
x = 2.566190379

Subproblem 2
x + -1.4 = -1.166190379

Simplifying
x + -1.4 = -1.166190379

Reorder the terms:
-1.4 + x = -1.166190379

Solving
-1.4 + x = -1.166190379

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = -1.166190379 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = -1.166190379 + 1.4
x = -1.166190379 + 1.4

Combine like terms: -1.166190379 + 1.4 = 0.233809621
x = 0.233809621

Simplifying
x = 0.233809621

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.566190379, 0.233809621}
Solution
x = {2.566190379, 0.233809621}