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

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

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

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

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

Reorder the terms:
2 + -6x = 4x(-5 + x) + 6
2 + -6x = (-5 * 4x + x * 4x) + 6
2 + -6x = (-20x + 4x2) + 6

Reorder the terms:
2 + -6x = 6 + -20x + 4x2

Solving
2 + -6x = 6 + -20x + 4x2

Solving for variable 'x'.

Reorder the terms:
2 + -6 + -6x + 20x + -4x2 = 6 + -20x + 4x2 + -6 + 20x + -4x2

Combine like terms: 2 + -6 = -4
-4 + -6x + 20x + -4x2 = 6 + -20x + 4x2 + -6 + 20x + -4x2

Combine like terms: -6x + 20x = 14x
-4 + 14x + -4x2 = 6 + -20x + 4x2 + -6 + 20x + -4x2

Reorder the terms:
-4 + 14x + -4x2 = 6 + -6 + -20x + 20x + 4x2 + -4x2

Combine like terms: 6 + -6 = 0
-4 + 14x + -4x2 = 0 + -20x + 20x + 4x2 + -4x2
-4 + 14x + -4x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
-4 + 14x + -4x2 = 0 + 4x2 + -4x2
-4 + 14x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-4 + 14x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 7x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + 7x + -2x2)' equal to zero and attempt to solve:

Simplifying
-2 + 7x + -2x2 = 0

Solving
-2 + 7x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -3.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.5x + x2 = 0 + -1
-3.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.5x + x2 = -1

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -1 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -1 + 3.0625

Combine like terms: -1 + 3.0625 = 2.0625
3.0625 + -3.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.436140662 and -1.436140662.

Subproblem 1
x + -1.75 = 1.436140662

Simplifying
x + -1.75 = 1.436140662

Reorder the terms:
-1.75 + x = 1.436140662

Solving
-1.75 + x = 1.436140662

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 1.436140662 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 1.436140662 + 1.75
x = 1.436140662 + 1.75

Combine like terms: 1.436140662 + 1.75 = 3.186140662
x = 3.186140662

Simplifying
x = 3.186140662

Subproblem 2
x + -1.75 = -1.436140662

Simplifying
x + -1.75 = -1.436140662

Reorder the terms:
-1.75 + x = -1.436140662

Solving
-1.75 + x = -1.436140662

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -1.436140662 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -1.436140662 + 1.75
x = -1.436140662 + 1.75

Combine like terms: -1.436140662 + 1.75 = 0.313859338
x = 0.313859338

Simplifying
x = 0.313859338

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.186140662, 0.313859338}
Solution
x = {3.186140662, 0.313859338}