7x(x-1)-3+5x=3(4x-3)+x

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

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

Reorder the terms:
7x(-1 + x) + -3 + 5x = 3(4x + -3) + x
(-1 * 7x + x * 7x) + -3 + 5x = 3(4x + -3) + x
(-7x + 7x2) + -3 + 5x = 3(4x + -3) + x

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

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

Reorder the terms:
-3 + -2x + 7x2 = 3(-3 + 4x) + x
-3 + -2x + 7x2 = (-3 * 3 + 4x * 3) + x
-3 + -2x + 7x2 = (-9 + 12x) + x

Combine like terms: 12x + x = 13x
-3 + -2x + 7x2 = -9 + 13x

Solving
-3 + -2x + 7x2 = -9 + 13x

Solving for variable 'x'.

Reorder the terms:
-3 + 9 + -2x + -13x + 7x2 = -9 + 13x + 9 + -13x

Combine like terms: -3 + 9 = 6
6 + -2x + -13x + 7x2 = -9 + 13x + 9 + -13x

Combine like terms: -2x + -13x = -15x
6 + -15x + 7x2 = -9 + 13x + 9 + -13x

Reorder the terms:
6 + -15x + 7x2 = -9 + 9 + 13x + -13x

Combine like terms: -9 + 9 = 0
6 + -15x + 7x2 = 0 + 13x + -13x
6 + -15x + 7x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
6 + -15x + 7x2 = 0

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

Divide each side by '7'.
0.8571428571 + -2.142857143x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + -2.142857143x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + -2.142857143x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + -2.142857143x + x2 = 0 + -0.8571428571
-2.142857143x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
-2.142857143x + x2 = -0.8571428571

The x term is -2.142857143x.  Take half its coefficient (-1.071428572).
Square it (1.147959185) and add it to both sides.

Add '1.147959185' to each side of the equation.
-2.142857143x + 1.147959185 + x2 = -0.8571428571 + 1.147959185

Reorder the terms:
1.147959185 + -2.142857143x + x2 = -0.8571428571 + 1.147959185

Combine like terms: -0.8571428571 + 1.147959185 = 0.2908163279
1.147959185 + -2.142857143x + x2 = 0.2908163279

Factor a perfect square on the left side:
(x + -1.071428572)(x + -1.071428572) = 0.2908163279

Calculate the square root of the right side: 0.53927389

Break this problem into two subproblems by setting 
(x + -1.071428572) equal to 0.53927389 and -0.53927389.

Subproblem 1
x + -1.071428572 = 0.53927389

Simplifying
x + -1.071428572 = 0.53927389

Reorder the terms:
-1.071428572 + x = 0.53927389

Solving
-1.071428572 + x = 0.53927389

Solving for variable 'x'.

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

Add '1.071428572' to each side of the equation.
-1.071428572 + 1.071428572 + x = 0.53927389 + 1.071428572

Combine like terms: -1.071428572 + 1.071428572 = 0.000000000
0.000000000 + x = 0.53927389 + 1.071428572
x = 0.53927389 + 1.071428572

Combine like terms: 0.53927389 + 1.071428572 = 1.610702462
x = 1.610702462

Simplifying
x = 1.610702462

Subproblem 2
x + -1.071428572 = -0.53927389

Simplifying
x + -1.071428572 = -0.53927389

Reorder the terms:
-1.071428572 + x = -0.53927389

Solving
-1.071428572 + x = -0.53927389

Solving for variable 'x'.

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

Add '1.071428572' to each side of the equation.
-1.071428572 + 1.071428572 + x = -0.53927389 + 1.071428572

Combine like terms: -1.071428572 + 1.071428572 = 0.000000000
0.000000000 + x = -0.53927389 + 1.071428572
x = -0.53927389 + 1.071428572

Combine like terms: -0.53927389 + 1.071428572 = 0.532154682
x = 0.532154682

Simplifying
x = 0.532154682

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.610702462, 0.532154682}