x(4x-2)+(3x-5)=(7x+5)(x-6)

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Solution for x(4x-2)+(3x-5)=(7x+5)(x-6) equation: 


Simplifying
x(4x + -2) + (3x + -5) = (7x + 5)(x + -6)

Reorder the terms:
x(-2 + 4x) + (3x + -5) = (7x + 5)(x + -6)
(-2 * x + 4x * x) + (3x + -5) = (7x + 5)(x + -6)
(-2x + 4x2) + (3x + -5) = (7x + 5)(x + -6)

Reorder the terms:
-2x + 4x2 + (-5 + 3x) = (7x + 5)(x + -6)

Remove parenthesis around (-5 + 3x)
-2x + 4x2 + -5 + 3x = (7x + 5)(x + -6)

Reorder the terms:
-5 + -2x + 3x + 4x2 = (7x + 5)(x + -6)

Combine like terms: -2x + 3x = 1x
-5 + 1x + 4x2 = (7x + 5)(x + -6)

Reorder the terms:
-5 + 1x + 4x2 = (5 + 7x)(x + -6)

Reorder the terms:
-5 + 1x + 4x2 = (5 + 7x)(-6 + x)

Multiply (5 + 7x) * (-6 + x)
-5 + 1x + 4x2 = (5(-6 + x) + 7x * (-6 + x))
-5 + 1x + 4x2 = ((-6 * 5 + x * 5) + 7x * (-6 + x))
-5 + 1x + 4x2 = ((-30 + 5x) + 7x * (-6 + x))
-5 + 1x + 4x2 = (-30 + 5x + (-6 * 7x + x * 7x))
-5 + 1x + 4x2 = (-30 + 5x + (-42x + 7x2))

Combine like terms: 5x + -42x = -37x
-5 + 1x + 4x2 = (-30 + -37x + 7x2)

Solving
-5 + 1x + 4x2 = -30 + -37x + 7x2

Solving for variable 'x'.

Reorder the terms:
-5 + 30 + 1x + 37x + 4x2 + -7x2 = -30 + -37x + 7x2 + 30 + 37x + -7x2

Combine like terms: -5 + 30 = 25
25 + 1x + 37x + 4x2 + -7x2 = -30 + -37x + 7x2 + 30 + 37x + -7x2

Combine like terms: 1x + 37x = 38x
25 + 38x + 4x2 + -7x2 = -30 + -37x + 7x2 + 30 + 37x + -7x2

Combine like terms: 4x2 + -7x2 = -3x2
25 + 38x + -3x2 = -30 + -37x + 7x2 + 30 + 37x + -7x2

Reorder the terms:
25 + 38x + -3x2 = -30 + 30 + -37x + 37x + 7x2 + -7x2

Combine like terms: -30 + 30 = 0
25 + 38x + -3x2 = 0 + -37x + 37x + 7x2 + -7x2
25 + 38x + -3x2 = -37x + 37x + 7x2 + -7x2

Combine like terms: -37x + 37x = 0
25 + 38x + -3x2 = 0 + 7x2 + -7x2
25 + 38x + -3x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
25 + 38x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-8.333333333 + -12.66666667x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + -12.66666667x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + -12.66666667x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + -12.66666667x + x2 = 0 + 8.333333333
-12.66666667x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
-12.66666667x + x2 = 8.333333333

The x term is -12.66666667x.  Take half its coefficient (-6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
-12.66666667x + 40.11111113 + x2 = 8.333333333 + 40.11111113

Reorder the terms:
40.11111113 + -12.66666667x + x2 = 8.333333333 + 40.11111113

Combine like terms: 8.333333333 + 40.11111113 = 48.444444463
40.11111113 + -12.66666667x + x2 = 48.444444463

Factor a perfect square on the left side:
(x + -6.333333335)(x + -6.333333335) = 48.444444463

Calculate the square root of the right side: 6.960204341

Break this problem into two subproblems by setting 
(x + -6.333333335) equal to 6.960204341 and -6.960204341.


Subproblem 1
x + -6.333333335 = 6.960204341

Simplifying
x + -6.333333335 = 6.960204341

Reorder the terms:
-6.333333335 + x = 6.960204341

Solving
-6.333333335 + x = 6.960204341

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = 6.960204341 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = 6.960204341 + 6.333333335
x = 6.960204341 + 6.333333335

Combine like terms: 6.960204341 + 6.333333335 = 13.293537676
x = 13.293537676

Simplifying
x = 13.293537676


Subproblem 2
x + -6.333333335 = -6.960204341

Simplifying
x + -6.333333335 = -6.960204341

Reorder the terms:
-6.333333335 + x = -6.960204341

Solving
-6.333333335 + x = -6.960204341

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = -6.960204341 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = -6.960204341 + 6.333333335
x = -6.960204341 + 6.333333335

Combine like terms: -6.960204341 + 6.333333335 = -0.626871006
x = -0.626871006

Simplifying
x = -0.626871006


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.293537676, -0.626871006}

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