-4[x(2x-3)-2(x+5)]+3x=-2(2x-3)

Solution for -4[x(2x-3)-2(x+5)]+3x=-2(2x-3) equation:

Simplifying
-4[x(2x + -3) + -2(x + 5)] + 3x = -2(2x + -3)

Reorder the terms:
-4[x(-3 + 2x) + -2(x + 5)] + 3x = -2(2x + -3)
-4[(-3 * x + 2x * x) + -2(x + 5)] + 3x = -2(2x + -3)
-4[(-3x + 2x2) + -2(x + 5)] + 3x = -2(2x + -3)

Reorder the terms:
-4[-3x + 2x2 + -2(5 + x)] + 3x = -2(2x + -3)
-4[-3x + 2x2 + (5 * -2 + x * -2)] + 3x = -2(2x + -3)
-4[-3x + 2x2 + (-10 + -2x)] + 3x = -2(2x + -3)

Reorder the terms:
-4[-10 + -3x + -2x + 2x2] + 3x = -2(2x + -3)

Combine like terms: -3x + -2x = -5x
-4[-10 + -5x + 2x2] + 3x = -2(2x + -3)
[-10 * -4 + -5x * -4 + 2x2 * -4] + 3x = -2(2x + -3)
[40 + 20x + -8x2] + 3x = -2(2x + -3)

Reorder the terms:
40 + 20x + 3x + -8x2 = -2(2x + -3)

Combine like terms: 20x + 3x = 23x
40 + 23x + -8x2 = -2(2x + -3)

Reorder the terms:
40 + 23x + -8x2 = -2(-3 + 2x)
40 + 23x + -8x2 = (-3 * -2 + 2x * -2)
40 + 23x + -8x2 = (6 + -4x)

Solving
40 + 23x + -8x2 = 6 + -4x

Solving for variable 'x'.

Reorder the terms:
40 + -6 + 23x + 4x + -8x2 = 6 + -4x + -6 + 4x

Combine like terms: 40 + -6 = 34
34 + 23x + 4x + -8x2 = 6 + -4x + -6 + 4x

Combine like terms: 23x + 4x = 27x
34 + 27x + -8x2 = 6 + -4x + -6 + 4x

Reorder the terms:
34 + 27x + -8x2 = 6 + -6 + -4x + 4x

Combine like terms: 6 + -6 = 0
34 + 27x + -8x2 = 0 + -4x + 4x
34 + 27x + -8x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
34 + 27x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-4.25 + -3.375x + x2 = 0

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + -3.375x + 4.25 + x2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + -3.375x + x2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + -3.375x + x2 = 0 + 4.25
-3.375x + x2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
-3.375x + x2 = 4.25

The x term is -3.375x.  Take half its coefficient (-1.6875).
Square it (2.84765625) and add it to both sides.

Add '2.84765625' to each side of the equation.
-3.375x + 2.84765625 + x2 = 4.25 + 2.84765625

Reorder the terms:
2.84765625 + -3.375x + x2 = 4.25 + 2.84765625

Combine like terms: 4.25 + 2.84765625 = 7.09765625
2.84765625 + -3.375x + x2 = 7.09765625

Factor a perfect square on the left side:
(x + -1.6875)(x + -1.6875) = 7.09765625

Calculate the square root of the right side: 2.664142686

Break this problem into two subproblems by setting 
(x + -1.6875) equal to 2.664142686 and -2.664142686.

Subproblem 1
x + -1.6875 = 2.664142686

Simplifying
x + -1.6875 = 2.664142686

Reorder the terms:
-1.6875 + x = 2.664142686

Solving
-1.6875 + x = 2.664142686

Solving for variable 'x'.

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

Add '1.6875' to each side of the equation.
-1.6875 + 1.6875 + x = 2.664142686 + 1.6875

Combine like terms: -1.6875 + 1.6875 = 0.0000
0.0000 + x = 2.664142686 + 1.6875
x = 2.664142686 + 1.6875

Combine like terms: 2.664142686 + 1.6875 = 4.351642686
x = 4.351642686

Simplifying
x = 4.351642686

Subproblem 2
x + -1.6875 = -2.664142686

Simplifying
x + -1.6875 = -2.664142686

Reorder the terms:
-1.6875 + x = -2.664142686

Solving
-1.6875 + x = -2.664142686

Solving for variable 'x'.

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

Add '1.6875' to each side of the equation.
-1.6875 + 1.6875 + x = -2.664142686 + 1.6875

Combine like terms: -1.6875 + 1.6875 = 0.0000
0.0000 + x = -2.664142686 + 1.6875
x = -2.664142686 + 1.6875

Combine like terms: -2.664142686 + 1.6875 = -0.976642686
x = -0.976642686

Simplifying
x = -0.976642686

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.351642686, -0.976642686}