2-3x(x-5)=4(x-1)

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

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

Reorder the terms:
2 + -3x(-5 + x) = 4(x + -1)
2 + (-5 * -3x + x * -3x) = 4(x + -1)
2 + (15x + -3x2) = 4(x + -1)

Reorder the terms:
2 + 15x + -3x2 = 4(-1 + x)
2 + 15x + -3x2 = (-1 * 4 + x * 4)
2 + 15x + -3x2 = (-4 + 4x)

Solving
2 + 15x + -3x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:
2 + 4 + 15x + -4x + -3x2 = -4 + 4x + 4 + -4x

Combine like terms: 2 + 4 = 6
6 + 15x + -4x + -3x2 = -4 + 4x + 4 + -4x

Combine like terms: 15x + -4x = 11x
6 + 11x + -3x2 = -4 + 4x + 4 + -4x

Reorder the terms:
6 + 11x + -3x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0
6 + 11x + -3x2 = 0 + 4x + -4x
6 + 11x + -3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
6 + 11x + -3x2 = 0

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

Divide each side by '-3'.
-2 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3.666666667x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3.666666667x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3.666666667x + x2 = 0 + 2
-3.666666667x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3.666666667x + x2 = 2

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 2 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 2 + 3.361111114

Combine like terms: 2 + 3.361111114 = 5.361111114
3.361111114 + -3.666666667x + x2 = 5.361111114

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 5.361111114

Calculate the square root of the right side: 2.315407332

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 2.315407332 and -2.315407332.

Subproblem 1
x + -1.833333334 = 2.315407332

Simplifying
x + -1.833333334 = 2.315407332

Reorder the terms:
-1.833333334 + x = 2.315407332

Solving
-1.833333334 + x = 2.315407332

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 2.315407332 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 2.315407332 + 1.833333334
x = 2.315407332 + 1.833333334

Combine like terms: 2.315407332 + 1.833333334 = 4.148740666
x = 4.148740666

Simplifying
x = 4.148740666

Subproblem 2
x + -1.833333334 = -2.315407332

Simplifying
x + -1.833333334 = -2.315407332

Reorder the terms:
-1.833333334 + x = -2.315407332

Solving
-1.833333334 + x = -2.315407332

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -2.315407332 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -2.315407332 + 1.833333334
x = -2.315407332 + 1.833333334

Combine like terms: -2.315407332 + 1.833333334 = -0.482073998
x = -0.482073998

Simplifying
x = -0.482073998

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.148740666, -0.482073998}