-4x[x-2-3(5-x)]-9+2x^2=

Solution for -4x[x-2-3(5-x)]-9+2x^2= equation:

Simplifying
-4x[x + -2 + -3(5 + -1x)] + -9 + 2x2 = 0
-4x[x + -2 + (5 * -3 + -1x * -3)] + -9 + 2x2 = 0
-4x[x + -2 + (-15 + 3x)] + -9 + 2x2 = 0

Reorder the terms:
-4x[-2 + -15 + x + 3x] + -9 + 2x2 = 0

Combine like terms: -2 + -15 = -17
-4x[-17 + x + 3x] + -9 + 2x2 = 0

Combine like terms: x + 3x = 4x
-4x[-17 + 4x] + -9 + 2x2 = 0
[-17 * -4x + 4x * -4x] + -9 + 2x2 = 0
[68x + -16x2] + -9 + 2x2 = 0

Reorder the terms:
-9 + 68x + -16x2 + 2x2 = 0

Combine like terms: -16x2 + 2x2 = -14x2
-9 + 68x + -14x2 = 0

Solving
-9 + 68x + -14x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
0.6428571429 + -4.857142857x + x2 = 0

Move the constant term to the right:

Add '-0.6428571429' to each side of the equation.
0.6428571429 + -4.857142857x + -0.6428571429 + x2 = 0 + -0.6428571429

Reorder the terms:
0.6428571429 + -0.6428571429 + -4.857142857x + x2 = 0 + -0.6428571429

Combine like terms: 0.6428571429 + -0.6428571429 = 0.0000000000
0.0000000000 + -4.857142857x + x2 = 0 + -0.6428571429
-4.857142857x + x2 = 0 + -0.6428571429

Combine like terms: 0 + -0.6428571429 = -0.6428571429
-4.857142857x + x2 = -0.6428571429

The x term is -4.857142857x.  Take half its coefficient (-2.428571429).
Square it (5.897959186) and add it to both sides.

Add '5.897959186' to each side of the equation.
-4.857142857x + 5.897959186 + x2 = -0.6428571429 + 5.897959186

Reorder the terms:
5.897959186 + -4.857142857x + x2 = -0.6428571429 + 5.897959186

Combine like terms: -0.6428571429 + 5.897959186 = 5.2551020431
5.897959186 + -4.857142857x + x2 = 5.2551020431

Factor a perfect square on the left side:
(x + -2.428571429)(x + -2.428571429) = 5.2551020431

Calculate the square root of the right side: 2.292400934

Break this problem into two subproblems by setting 
(x + -2.428571429) equal to 2.292400934 and -2.292400934.

Subproblem 1
x + -2.428571429 = 2.292400934

Simplifying
x + -2.428571429 = 2.292400934

Reorder the terms:
-2.428571429 + x = 2.292400934

Solving
-2.428571429 + x = 2.292400934

Solving for variable 'x'.

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

Add '2.428571429' to each side of the equation.
-2.428571429 + 2.428571429 + x = 2.292400934 + 2.428571429

Combine like terms: -2.428571429 + 2.428571429 = 0.000000000
0.000000000 + x = 2.292400934 + 2.428571429
x = 2.292400934 + 2.428571429

Combine like terms: 2.292400934 + 2.428571429 = 4.720972363
x = 4.720972363

Simplifying
x = 4.720972363

Subproblem 2
x + -2.428571429 = -2.292400934

Simplifying
x + -2.428571429 = -2.292400934

Reorder the terms:
-2.428571429 + x = -2.292400934

Solving
-2.428571429 + x = -2.292400934

Solving for variable 'x'.

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

Add '2.428571429' to each side of the equation.
-2.428571429 + 2.428571429 + x = -2.292400934 + 2.428571429

Combine like terms: -2.428571429 + 2.428571429 = 0.000000000
0.000000000 + x = -2.292400934 + 2.428571429
x = -2.292400934 + 2.428571429

Combine like terms: -2.292400934 + 2.428571429 = 0.136170495
x = 0.136170495

Simplifying
x = 0.136170495

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.720972363, 0.136170495}