2[-(x-1)+4]=5x[-(6x-7)+9x]

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Solution for 2[-(x-1)+4]=5x[-(6x-7)+9x] equation: 


Simplifying
2[-1(x + -1) + 4] = 5x[-1(6x + -7) + 9x]

Reorder the terms:
2[-1(-1 + x) + 4] = 5x[-1(6x + -7) + 9x]
2[(-1 * -1 + x * -1) + 4] = 5x[-1(6x + -7) + 9x]
2[(1 + -1x) + 4] = 5x[-1(6x + -7) + 9x]

Reorder the terms:
2[1 + 4 + -1x] = 5x[-1(6x + -7) + 9x]

Combine like terms: 1 + 4 = 5
2[5 + -1x] = 5x[-1(6x + -7) + 9x]
[5 * 2 + -1x * 2] = 5x[-1(6x + -7) + 9x]
[10 + -2x] = 5x[-1(6x + -7) + 9x]

Reorder the terms:
10 + -2x = 5x[-1(-7 + 6x) + 9x]
10 + -2x = 5x[(-7 * -1 + 6x * -1) + 9x]
10 + -2x = 5x[(7 + -6x) + 9x]

Combine like terms: -6x + 9x = 3x
10 + -2x = 5x[7 + 3x]
10 + -2x = [7 * 5x + 3x * 5x]
10 + -2x = [35x + 15x2]

Solving
10 + -2x = 35x + 15x2

Solving for variable 'x'.

Combine like terms: -2x + -35x = -37x
10 + -37x + -15x2 = 35x + 15x2 + -35x + -15x2

Reorder the terms:
10 + -37x + -15x2 = 35x + -35x + 15x2 + -15x2

Combine like terms: 35x + -35x = 0
10 + -37x + -15x2 = 0 + 15x2 + -15x2
10 + -37x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
10 + -37x + -15x2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-0.6666666667 + 2.466666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 2.466666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 2.466666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 2.466666667x + x2 = 0 + 0.6666666667
2.466666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
2.466666667x + x2 = 0.6666666667

The x term is 2.466666667x.  Take half its coefficient (1.233333334).
Square it (1.521111113) and add it to both sides.

Add '1.521111113' to each side of the equation.
2.466666667x + 1.521111113 + x2 = 0.6666666667 + 1.521111113

Reorder the terms:
1.521111113 + 2.466666667x + x2 = 0.6666666667 + 1.521111113

Combine like terms: 0.6666666667 + 1.521111113 = 2.1877777797
1.521111113 + 2.466666667x + x2 = 2.1877777797

Factor a perfect square on the left side:
(x + 1.233333334)(x + 1.233333334) = 2.1877777797

Calculate the square root of the right side: 1.479113849

Break this problem into two subproblems by setting 
(x + 1.233333334) equal to 1.479113849 and -1.479113849.


Subproblem 1
x + 1.233333334 = 1.479113849

Simplifying
x + 1.233333334 = 1.479113849

Reorder the terms:
1.233333334 + x = 1.479113849

Solving
1.233333334 + x = 1.479113849

Solving for variable 'x'.

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

Add '-1.233333334' to each side of the equation.
1.233333334 + -1.233333334 + x = 1.479113849 + -1.233333334

Combine like terms: 1.233333334 + -1.233333334 = 0.000000000
0.000000000 + x = 1.479113849 + -1.233333334
x = 1.479113849 + -1.233333334

Combine like terms: 1.479113849 + -1.233333334 = 0.245780515
x = 0.245780515

Simplifying
x = 0.245780515


Subproblem 2
x + 1.233333334 = -1.479113849

Simplifying
x + 1.233333334 = -1.479113849

Reorder the terms:
1.233333334 + x = -1.479113849

Solving
1.233333334 + x = -1.479113849

Solving for variable 'x'.

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

Add '-1.233333334' to each side of the equation.
1.233333334 + -1.233333334 + x = -1.479113849 + -1.233333334

Combine like terms: 1.233333334 + -1.233333334 = 0.000000000
0.000000000 + x = -1.479113849 + -1.233333334
x = -1.479113849 + -1.233333334

Combine like terms: -1.479113849 + -1.233333334 = -2.712447183
x = -2.712447183

Simplifying
x = -2.712447183


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.245780515, -2.712447183}

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