5x[7-(2x-1)]=3(x-5)+4(x+3)

Solution for 5x[7-(2x-1)]=3(x-5)+4(x+3) equation:

Simplifying
5x[7 + -1(2x + -1)] = 3(x + -5) + 4(x + 3)

Reorder the terms:
5x[7 + -1(-1 + 2x)] = 3(x + -5) + 4(x + 3)
5x[7 + (-1 * -1 + 2x * -1)] = 3(x + -5) + 4(x + 3)
5x[7 + (1 + -2x)] = 3(x + -5) + 4(x + 3)

Combine like terms: 7 + 1 = 8
5x[8 + -2x] = 3(x + -5) + 4(x + 3)
[8 * 5x + -2x * 5x] = 3(x + -5) + 4(x + 3)
[40x + -10x2] = 3(x + -5) + 4(x + 3)

Reorder the terms:
40x + -10x2 = 3(-5 + x) + 4(x + 3)
40x + -10x2 = (-5 * 3 + x * 3) + 4(x + 3)
40x + -10x2 = (-15 + 3x) + 4(x + 3)

Reorder the terms:
40x + -10x2 = -15 + 3x + 4(3 + x)
40x + -10x2 = -15 + 3x + (3 * 4 + x * 4)
40x + -10x2 = -15 + 3x + (12 + 4x)

Reorder the terms:
40x + -10x2 = -15 + 12 + 3x + 4x

Combine like terms: -15 + 12 = -3
40x + -10x2 = -3 + 3x + 4x

Combine like terms: 3x + 4x = 7x
40x + -10x2 = -3 + 7x

Solving
40x + -10x2 = -3 + 7x

Solving for variable 'x'.

Reorder the terms:
3 + 40x + -7x + -10x2 = -3 + 7x + 3 + -7x

Combine like terms: 40x + -7x = 33x
3 + 33x + -10x2 = -3 + 7x + 3 + -7x

Reorder the terms:
3 + 33x + -10x2 = -3 + 3 + 7x + -7x

Combine like terms: -3 + 3 = 0
3 + 33x + -10x2 = 0 + 7x + -7x
3 + 33x + -10x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
3 + 33x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.3 + -3.3x + x2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + -3.3x + 0.3 + x2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + -3.3x + x2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + -3.3x + x2 = 0.0 + 0.3
-3.3x + x2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
-3.3x + x2 = 0.3

The x term is -3.3x.  Take half its coefficient (-1.65).
Square it (2.7225) and add it to both sides.

Add '2.7225' to each side of the equation.
-3.3x + 2.7225 + x2 = 0.3 + 2.7225

Reorder the terms:
2.7225 + -3.3x + x2 = 0.3 + 2.7225

Combine like terms: 0.3 + 2.7225 = 3.0225
2.7225 + -3.3x + x2 = 3.0225

Factor a perfect square on the left side:
(x + -1.65)(x + -1.65) = 3.0225

Calculate the square root of the right side: 1.738533865

Break this problem into two subproblems by setting 
(x + -1.65) equal to 1.738533865 and -1.738533865.

Subproblem 1
x + -1.65 = 1.738533865

Simplifying
x + -1.65 = 1.738533865

Reorder the terms:
-1.65 + x = 1.738533865

Solving
-1.65 + x = 1.738533865

Solving for variable 'x'.

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

Add '1.65' to each side of the equation.
-1.65 + 1.65 + x = 1.738533865 + 1.65

Combine like terms: -1.65 + 1.65 = 0.00
0.00 + x = 1.738533865 + 1.65
x = 1.738533865 + 1.65

Combine like terms: 1.738533865 + 1.65 = 3.388533865
x = 3.388533865

Simplifying
x = 3.388533865

Subproblem 2
x + -1.65 = -1.738533865

Simplifying
x + -1.65 = -1.738533865

Reorder the terms:
-1.65 + x = -1.738533865

Solving
-1.65 + x = -1.738533865

Solving for variable 'x'.

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

Add '1.65' to each side of the equation.
-1.65 + 1.65 + x = -1.738533865 + 1.65

Combine like terms: -1.65 + 1.65 = 0.00
0.00 + x = -1.738533865 + 1.65
x = -1.738533865 + 1.65

Combine like terms: -1.738533865 + 1.65 = -0.088533865
x = -0.088533865

Simplifying
x = -0.088533865

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.388533865, -0.088533865}