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

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

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

Reorder the terms:
x = (-3 + 3x)(2x + -5)

Reorder the terms:
x = (-3 + 3x)(-5 + 2x)

Multiply (-3 + 3x) * (-5 + 2x)
x = (-3(-5 + 2x) + 3x * (-5 + 2x))
x = ((-5 * -3 + 2x * -3) + 3x * (-5 + 2x))
x = ((15 + -6x) + 3x * (-5 + 2x))
x = (15 + -6x + (-5 * 3x + 2x * 3x))
x = (15 + -6x + (-15x + 6x2))

Combine like terms: -6x + -15x = -21x
x = (15 + -21x + 6x2)

Solving
x = 15 + -21x + 6x2

Solving for variable 'x'.

Reorder the terms:
-15 + x + 21x + -6x2 = 15 + -21x + 6x2 + -15 + 21x + -6x2

Combine like terms: x + 21x = 22x
-15 + 22x + -6x2 = 15 + -21x + 6x2 + -15 + 21x + -6x2

Reorder the terms:
-15 + 22x + -6x2 = 15 + -15 + -21x + 21x + 6x2 + -6x2

Combine like terms: 15 + -15 = 0
-15 + 22x + -6x2 = 0 + -21x + 21x + 6x2 + -6x2
-15 + 22x + -6x2 = -21x + 21x + 6x2 + -6x2

Combine like terms: -21x + 21x = 0
-15 + 22x + -6x2 = 0 + 6x2 + -6x2
-15 + 22x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-15 + 22x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
2.5 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -3.666666667x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -3.666666667x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -3.666666667x + x2 = 0 + -2.5
-3.666666667x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-3.666666667x + x2 = -2.5

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 = -2.5 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -2.5 + 3.361111114

Combine like terms: -2.5 + 3.361111114 = 0.861111114
3.361111114 + -3.666666667x + x2 = 0.861111114

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 0.861111114

Calculate the square root of the right side: 0.927960729

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 0.927960729 and -0.927960729.

Subproblem 1
x + -1.833333334 = 0.927960729

Simplifying
x + -1.833333334 = 0.927960729

Reorder the terms:
-1.833333334 + x = 0.927960729

Solving
-1.833333334 + x = 0.927960729

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 = 0.927960729 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 0.927960729 + 1.833333334
x = 0.927960729 + 1.833333334

Combine like terms: 0.927960729 + 1.833333334 = 2.761294063
x = 2.761294063

Simplifying
x = 2.761294063

Subproblem 2
x + -1.833333334 = -0.927960729

Simplifying
x + -1.833333334 = -0.927960729

Reorder the terms:
-1.833333334 + x = -0.927960729

Solving
-1.833333334 + x = -0.927960729

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 = -0.927960729 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -0.927960729 + 1.833333334
x = -0.927960729 + 1.833333334

Combine like terms: -0.927960729 + 1.833333334 = 0.905372605
x = 0.905372605

Simplifying
x = 0.905372605

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.761294063, 0.905372605}