5(-4x+2)-(x-3)*4(6x-5)+16x=

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Solution for 5(-4x+2)-(x-3)*4(6x-5)+16x= equation: 


Simplifying
5(-4x + 2) + -1(x + -3) * 4(6x + -5) + 16x = 0

Reorder the terms:
5(2 + -4x) + -1(x + -3) * 4(6x + -5) + 16x = 0
(2 * 5 + -4x * 5) + -1(x + -3) * 4(6x + -5) + 16x = 0
(10 + -20x) + -1(x + -3) * 4(6x + -5) + 16x = 0

Reorder the terms:
10 + -20x + -1(-3 + x) * 4(6x + -5) + 16x = 0

Reorder the terms:
10 + -20x + -1(-3 + x) * 4(-5 + 6x) + 16x = 0

Reorder the terms for easier multiplication:
10 + -20x + -1 * 4(-3 + x)(-5 + 6x) + 16x = 0

Multiply -1 * 4
10 + -20x + -4(-3 + x)(-5 + 6x) + 16x = 0

Multiply (-3 + x) * (-5 + 6x)
10 + -20x + -4(-3(-5 + 6x) + x(-5 + 6x)) + 16x = 0
10 + -20x + -4((-5 * -3 + 6x * -3) + x(-5 + 6x)) + 16x = 0
10 + -20x + -4((15 + -18x) + x(-5 + 6x)) + 16x = 0
10 + -20x + -4(15 + -18x + (-5 * x + 6x * x)) + 16x = 0
10 + -20x + -4(15 + -18x + (-5x + 6x2)) + 16x = 0

Combine like terms: -18x + -5x = -23x
10 + -20x + -4(15 + -23x + 6x2) + 16x = 0
10 + -20x + (15 * -4 + -23x * -4 + 6x2 * -4) + 16x = 0
10 + -20x + (-60 + 92x + -24x2) + 16x = 0

Reorder the terms:
10 + -60 + -20x + 92x + 16x + -24x2 = 0

Combine like terms: 10 + -60 = -50
-50 + -20x + 92x + 16x + -24x2 = 0

Combine like terms: -20x + 92x = 72x
-50 + 72x + 16x + -24x2 = 0

Combine like terms: 72x + 16x = 88x
-50 + 88x + -24x2 = 0

Solving
-50 + 88x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 44x + -12x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + 44x + -12x2)' equal to zero and attempt to solve:

Simplifying
-25 + 44x + -12x2 = 0

Solving
-25 + 44x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
2.083333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.083333333' to each side of the equation.
2.083333333 + -3.666666667x + -2.083333333 + x2 = 0 + -2.083333333

Reorder the terms:
2.083333333 + -2.083333333 + -3.666666667x + x2 = 0 + -2.083333333

Combine like terms: 2.083333333 + -2.083333333 = 0.000000000
0.000000000 + -3.666666667x + x2 = 0 + -2.083333333
-3.666666667x + x2 = 0 + -2.083333333

Combine like terms: 0 + -2.083333333 = -2.083333333
-3.666666667x + x2 = -2.083333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = -2.083333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -2.083333333 + 3.361111114

Combine like terms: -2.083333333 + 3.361111114 = 1.277777781
3.361111114 + -3.666666667x + x2 = 1.277777781

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 1.277777781

Calculate the square root of the right side: 1.130388332

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 1.130388332 and -1.130388332.


Subproblem 1
x + -1.833333334 = 1.130388332

Simplifying
x + -1.833333334 = 1.130388332

Reorder the terms:
-1.833333334 + x = 1.130388332

Solving
-1.833333334 + x = 1.130388332

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 1.130388332 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 1.130388332 + 1.833333334
x = 1.130388332 + 1.833333334

Combine like terms: 1.130388332 + 1.833333334 = 2.963721666
x = 2.963721666

Simplifying
x = 2.963721666


Subproblem 2
x + -1.833333334 = -1.130388332

Simplifying
x + -1.833333334 = -1.130388332

Reorder the terms:
-1.833333334 + x = -1.130388332

Solving
-1.833333334 + x = -1.130388332

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -1.130388332 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -1.130388332 + 1.833333334
x = -1.130388332 + 1.833333334

Combine like terms: -1.130388332 + 1.833333334 = 0.702945002
x = 0.702945002

Simplifying
x = 0.702945002


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.963721666, 0.702945002}
Solution
x = {2.963721666, 0.702945002}

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