6(10-x)=3(3x-5)9(2x-1)

Solution for 6(10-x)=3(3x-5)9(2x-1) equation:

Simplifying
6(10 + -1x) = 3(3x + -5) * 9(2x + -1)
(10 * 6 + -1x * 6) = 3(3x + -5) * 9(2x + -1)
(60 + -6x) = 3(3x + -5) * 9(2x + -1)

Reorder the terms:
60 + -6x = 3(-5 + 3x) * 9(2x + -1)

Reorder the terms:
60 + -6x = 3(-5 + 3x) * 9(-1 + 2x)

Reorder the terms for easier multiplication:
60 + -6x = 3 * 9(-5 + 3x)(-1 + 2x)

Multiply 3 * 9
60 + -6x = 27(-5 + 3x)(-1 + 2x)

Multiply (-5 + 3x) * (-1 + 2x)
60 + -6x = 27(-5(-1 + 2x) + 3x * (-1 + 2x))
60 + -6x = 27((-1 * -5 + 2x * -5) + 3x * (-1 + 2x))
60 + -6x = 27((5 + -10x) + 3x * (-1 + 2x))
60 + -6x = 27(5 + -10x + (-1 * 3x + 2x * 3x))
60 + -6x = 27(5 + -10x + (-3x + 6x2))

Combine like terms: -10x + -3x = -13x
60 + -6x = 27(5 + -13x + 6x2)
60 + -6x = (5 * 27 + -13x * 27 + 6x2 * 27)
60 + -6x = (135 + -351x + 162x2)

Solving
60 + -6x = 135 + -351x + 162x2

Solving for variable 'x'.

Reorder the terms:
60 + -135 + -6x + 351x + -162x2 = 135 + -351x + 162x2 + -135 + 351x + -162x2

Combine like terms: 60 + -135 = -75
-75 + -6x + 351x + -162x2 = 135 + -351x + 162x2 + -135 + 351x + -162x2

Combine like terms: -6x + 351x = 345x
-75 + 345x + -162x2 = 135 + -351x + 162x2 + -135 + 351x + -162x2

Reorder the terms:
-75 + 345x + -162x2 = 135 + -135 + -351x + 351x + 162x2 + -162x2

Combine like terms: 135 + -135 = 0
-75 + 345x + -162x2 = 0 + -351x + 351x + 162x2 + -162x2
-75 + 345x + -162x2 = -351x + 351x + 162x2 + -162x2

Combine like terms: -351x + 351x = 0
-75 + 345x + -162x2 = 0 + 162x2 + -162x2
-75 + 345x + -162x2 = 162x2 + -162x2

Combine like terms: 162x2 + -162x2 = 0
-75 + 345x + -162x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + 115x + -54x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-25 + 115x + -54x2)' equal to zero and attempt to solve:

Simplifying
-25 + 115x + -54x2 = 0

Solving
-25 + 115x + -54x2 = 0

Begin completing the square.  Divide all terms by
-54 the coefficient of the squared term: 

Divide each side by '-54'.
0.462962963 + -2.12962963x + x2 = 0

Move the constant term to the right:

Add '-0.462962963' to each side of the equation.
0.462962963 + -2.12962963x + -0.462962963 + x2 = 0 + -0.462962963

Reorder the terms:
0.462962963 + -0.462962963 + -2.12962963x + x2 = 0 + -0.462962963

Combine like terms: 0.462962963 + -0.462962963 = 0.000000000
0.000000000 + -2.12962963x + x2 = 0 + -0.462962963
-2.12962963x + x2 = 0 + -0.462962963

Combine like terms: 0 + -0.462962963 = -0.462962963
-2.12962963x + x2 = -0.462962963

The x term is -2.12962963x.  Take half its coefficient (-1.064814815).
Square it (1.133830590) and add it to both sides.

Add '1.133830590' to each side of the equation.
-2.12962963x + 1.133830590 + x2 = -0.462962963 + 1.133830590

Reorder the terms:
1.133830590 + -2.12962963x + x2 = -0.462962963 + 1.133830590

Combine like terms: -0.462962963 + 1.133830590 = 0.670867627
1.133830590 + -2.12962963x + x2 = 0.670867627

Factor a perfect square on the left side:
(x + -1.064814815)(x + -1.064814815) = 0.670867627

Calculate the square root of the right side: 0.819065093

Break this problem into two subproblems by setting 
(x + -1.064814815) equal to 0.819065093 and -0.819065093.

Subproblem 1
x + -1.064814815 = 0.819065093

Simplifying
x + -1.064814815 = 0.819065093

Reorder the terms:
-1.064814815 + x = 0.819065093

Solving
-1.064814815 + x = 0.819065093

Solving for variable 'x'.

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

Add '1.064814815' to each side of the equation.
-1.064814815 + 1.064814815 + x = 0.819065093 + 1.064814815

Combine like terms: -1.064814815 + 1.064814815 = 0.000000000
0.000000000 + x = 0.819065093 + 1.064814815
x = 0.819065093 + 1.064814815

Combine like terms: 0.819065093 + 1.064814815 = 1.883879908
x = 1.883879908

Simplifying
x = 1.883879908

Subproblem 2
x + -1.064814815 = -0.819065093

Simplifying
x + -1.064814815 = -0.819065093

Reorder the terms:
-1.064814815 + x = -0.819065093

Solving
-1.064814815 + x = -0.819065093

Solving for variable 'x'.

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

Add '1.064814815' to each side of the equation.
-1.064814815 + 1.064814815 + x = -0.819065093 + 1.064814815

Combine like terms: -1.064814815 + 1.064814815 = 0.000000000
0.000000000 + x = -0.819065093 + 1.064814815
x = -0.819065093 + 1.064814815

Combine like terms: -0.819065093 + 1.064814815 = 0.245749722
x = 0.245749722

Simplifying
x = 0.245749722

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.883879908, 0.245749722}
Solution
x = {1.883879908, 0.245749722}