4x-(2x+3)-(3x-5)=49-(6x-1)(x-2)

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Solution for 4x-(2x+3)-(3x-5)=49-(6x-1)(x-2) equation: 


Simplifying
4x + -1(2x + 3) + -1(3x + -5) = 49 + -1(6x + -1)(x + -2)

Reorder the terms:
4x + -1(3 + 2x) + -1(3x + -5) = 49 + -1(6x + -1)(x + -2)
4x + (3 * -1 + 2x * -1) + -1(3x + -5) = 49 + -1(6x + -1)(x + -2)
4x + (-3 + -2x) + -1(3x + -5) = 49 + -1(6x + -1)(x + -2)

Reorder the terms:
4x + -3 + -2x + -1(-5 + 3x) = 49 + -1(6x + -1)(x + -2)
4x + -3 + -2x + (-5 * -1 + 3x * -1) = 49 + -1(6x + -1)(x + -2)
4x + -3 + -2x + (5 + -3x) = 49 + -1(6x + -1)(x + -2)

Reorder the terms:
-3 + 5 + 4x + -2x + -3x = 49 + -1(6x + -1)(x + -2)

Combine like terms: -3 + 5 = 2
2 + 4x + -2x + -3x = 49 + -1(6x + -1)(x + -2)

Combine like terms: 4x + -2x = 2x
2 + 2x + -3x = 49 + -1(6x + -1)(x + -2)

Combine like terms: 2x + -3x = -1x
2 + -1x = 49 + -1(6x + -1)(x + -2)

Reorder the terms:
2 + -1x = 49 + -1(-1 + 6x)(x + -2)

Reorder the terms:
2 + -1x = 49 + -1(-1 + 6x)(-2 + x)

Multiply (-1 + 6x) * (-2 + x)
2 + -1x = 49 + -1(-1(-2 + x) + 6x * (-2 + x))
2 + -1x = 49 + -1((-2 * -1 + x * -1) + 6x * (-2 + x))
2 + -1x = 49 + -1((2 + -1x) + 6x * (-2 + x))
2 + -1x = 49 + -1(2 + -1x + (-2 * 6x + x * 6x))
2 + -1x = 49 + -1(2 + -1x + (-12x + 6x2))

Combine like terms: -1x + -12x = -13x
2 + -1x = 49 + -1(2 + -13x + 6x2)
2 + -1x = 49 + (2 * -1 + -13x * -1 + 6x2 * -1)
2 + -1x = 49 + (-2 + 13x + -6x2)

Combine like terms: 49 + -2 = 47
2 + -1x = 47 + 13x + -6x2

Solving
2 + -1x = 47 + 13x + -6x2

Solving for variable 'x'.

Reorder the terms:
2 + -47 + -1x + -13x + 6x2 = 47 + 13x + -6x2 + -47 + -13x + 6x2

Combine like terms: 2 + -47 = -45
-45 + -1x + -13x + 6x2 = 47 + 13x + -6x2 + -47 + -13x + 6x2

Combine like terms: -1x + -13x = -14x
-45 + -14x + 6x2 = 47 + 13x + -6x2 + -47 + -13x + 6x2

Reorder the terms:
-45 + -14x + 6x2 = 47 + -47 + 13x + -13x + -6x2 + 6x2

Combine like terms: 47 + -47 = 0
-45 + -14x + 6x2 = 0 + 13x + -13x + -6x2 + 6x2
-45 + -14x + 6x2 = 13x + -13x + -6x2 + 6x2

Combine like terms: 13x + -13x = 0
-45 + -14x + 6x2 = 0 + -6x2 + 6x2
-45 + -14x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-45 + -14x + 6x2 = 0

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

Divide each side by '6'.
-7.5 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -2.333333333x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -2.333333333x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -2.333333333x + x2 = 0 + 7.5
-2.333333333x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-2.333333333x + x2 = 7.5

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 7.5 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 7.5 + 1.361111112

Combine like terms: 7.5 + 1.361111112 = 8.861111112
1.361111112 + -2.333333333x + x2 = 8.861111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 8.861111112

Calculate the square root of the right side: 2.97676185

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 2.97676185 and -2.97676185.


Subproblem 1
x + -1.166666667 = 2.97676185

Simplifying
x + -1.166666667 = 2.97676185

Reorder the terms:
-1.166666667 + x = 2.97676185

Solving
-1.166666667 + x = 2.97676185

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 2.97676185 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 2.97676185 + 1.166666667
x = 2.97676185 + 1.166666667

Combine like terms: 2.97676185 + 1.166666667 = 4.143428517
x = 4.143428517

Simplifying
x = 4.143428517


Subproblem 2
x + -1.166666667 = -2.97676185

Simplifying
x + -1.166666667 = -2.97676185

Reorder the terms:
-1.166666667 + x = -2.97676185

Solving
-1.166666667 + x = -2.97676185

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -2.97676185 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -2.97676185 + 1.166666667
x = -2.97676185 + 1.166666667

Combine like terms: -2.97676185 + 1.166666667 = -1.810095183
x = -1.810095183

Simplifying
x = -1.810095183


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.143428517, -1.810095183}

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