4x(x-10)=-6(2-x)-6

Solution for 4x(x-10)=-6(2-x)-6 equation:

Simplifying
4x(x + -10) = -6(2 + -1x) + -6

Reorder the terms:
4x(-10 + x) = -6(2 + -1x) + -6
(-10 * 4x + x * 4x) = -6(2 + -1x) + -6
(-40x + 4x2) = -6(2 + -1x) + -6
-40x + 4x2 = (2 * -6 + -1x * -6) + -6
-40x + 4x2 = (-12 + 6x) + -6

Reorder the terms:
-40x + 4x2 = -12 + -6 + 6x

Combine like terms: -12 + -6 = -18
-40x + 4x2 = -18 + 6x

Solving
-40x + 4x2 = -18 + 6x

Solving for variable 'x'.

Reorder the terms:
18 + -40x + -6x + 4x2 = -18 + 6x + 18 + -6x

Combine like terms: -40x + -6x = -46x
18 + -46x + 4x2 = -18 + 6x + 18 + -6x

Reorder the terms:
18 + -46x + 4x2 = -18 + 18 + 6x + -6x

Combine like terms: -18 + 18 = 0
18 + -46x + 4x2 = 0 + 6x + -6x
18 + -46x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
18 + -46x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -23x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + -23x + 2x2)' equal to zero and attempt to solve:

Simplifying
9 + -23x + 2x2 = 0

Solving
9 + -23x + 2x2 = 0

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

Divide each side by '2'.
4.5 + -11.5x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -11.5x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -11.5x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -11.5x + x2 = 0 + -4.5
-11.5x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-11.5x + x2 = -4.5

The x term is -11.5x.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5x + 33.0625 + x2 = -4.5 + 33.0625

Reorder the terms:
33.0625 + -11.5x + x2 = -4.5 + 33.0625

Combine like terms: -4.5 + 33.0625 = 28.5625
33.0625 + -11.5x + x2 = 28.5625

Factor a perfect square on the left side:
(x + -5.75)(x + -5.75) = 28.5625

Calculate the square root of the right side: 5.344389582

Break this problem into two subproblems by setting 
(x + -5.75) equal to 5.344389582 and -5.344389582.

Subproblem 1
x + -5.75 = 5.344389582

Simplifying
x + -5.75 = 5.344389582

Reorder the terms:
-5.75 + x = 5.344389582

Solving
-5.75 + x = 5.344389582

Solving for variable 'x'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = 5.344389582 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = 5.344389582 + 5.75
x = 5.344389582 + 5.75

Combine like terms: 5.344389582 + 5.75 = 11.094389582
x = 11.094389582

Simplifying
x = 11.094389582

Subproblem 2
x + -5.75 = -5.344389582

Simplifying
x + -5.75 = -5.344389582

Reorder the terms:
-5.75 + x = -5.344389582

Solving
-5.75 + x = -5.344389582

Solving for variable 'x'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = -5.344389582 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = -5.344389582 + 5.75
x = -5.344389582 + 5.75

Combine like terms: -5.344389582 + 5.75 = 0.405610418
x = 0.405610418

Simplifying
x = 0.405610418

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.094389582, 0.405610418}
Solution
x = {11.094389582, 0.405610418}