4x=3(2-9x)8(x-1)

Solution for 4x=3(2-9x)8(x-1) equation:

Simplifying
4x = 3(2 + -9x) * 8(x + -1)

Reorder the terms:
4x = 3(2 + -9x) * 8(-1 + x)

Reorder the terms for easier multiplication:
4x = 3 * 8(2 + -9x)(-1 + x)

Multiply 3 * 8
4x = 24(2 + -9x)(-1 + x)

Multiply (2 + -9x) * (-1 + x)
4x = 24(2(-1 + x) + -9x * (-1 + x))
4x = 24((-1 * 2 + x * 2) + -9x * (-1 + x))
4x = 24((-2 + 2x) + -9x * (-1 + x))
4x = 24(-2 + 2x + (-1 * -9x + x * -9x))
4x = 24(-2 + 2x + (9x + -9x2))

Combine like terms: 2x + 9x = 11x
4x = 24(-2 + 11x + -9x2)
4x = (-2 * 24 + 11x * 24 + -9x2 * 24)
4x = (-48 + 264x + -216x2)

Solving
4x = -48 + 264x + -216x2

Solving for variable 'x'.

Reorder the terms:
48 + 4x + -264x + 216x2 = -48 + 264x + -216x2 + 48 + -264x + 216x2

Combine like terms: 4x + -264x = -260x
48 + -260x + 216x2 = -48 + 264x + -216x2 + 48 + -264x + 216x2

Reorder the terms:
48 + -260x + 216x2 = -48 + 48 + 264x + -264x + -216x2 + 216x2

Combine like terms: -48 + 48 = 0
48 + -260x + 216x2 = 0 + 264x + -264x + -216x2 + 216x2
48 + -260x + 216x2 = 264x + -264x + -216x2 + 216x2

Combine like terms: 264x + -264x = 0
48 + -260x + 216x2 = 0 + -216x2 + 216x2
48 + -260x + 216x2 = -216x2 + 216x2

Combine like terms: -216x2 + 216x2 = 0
48 + -260x + 216x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + -65x + 54x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(12 + -65x + 54x2)' equal to zero and attempt to solve:

Simplifying
12 + -65x + 54x2 = 0

Solving
12 + -65x + 54x2 = 0

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

Divide each side by '54'.
0.2222222222 + -1.203703704x + x2 = 0

Move the constant term to the right:

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -1.203703704x + -0.2222222222 + x2 = 0 + -0.2222222222

Reorder the terms:
0.2222222222 + -0.2222222222 + -1.203703704x + x2 = 0 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + -1.203703704x + x2 = 0 + -0.2222222222
-1.203703704x + x2 = 0 + -0.2222222222

Combine like terms: 0 + -0.2222222222 = -0.2222222222
-1.203703704x + x2 = -0.2222222222

The x term is -1.203703704x.  Take half its coefficient (-0.601851852).
Square it (0.3622256518) and add it to both sides.

Add '0.3622256518' to each side of the equation.
-1.203703704x + 0.3622256518 + x2 = -0.2222222222 + 0.3622256518

Reorder the terms:
0.3622256518 + -1.203703704x + x2 = -0.2222222222 + 0.3622256518

Combine like terms: -0.2222222222 + 0.3622256518 = 0.1400034296
0.3622256518 + -1.203703704x + x2 = 0.1400034296

Factor a perfect square on the left side:
(x + -0.601851852)(x + -0.601851852) = 0.1400034296

Calculate the square root of the right side: 0.374170322

Break this problem into two subproblems by setting 
(x + -0.601851852) equal to 0.374170322 and -0.374170322.

Subproblem 1
x + -0.601851852 = 0.374170322

Simplifying
x + -0.601851852 = 0.374170322

Reorder the terms:
-0.601851852 + x = 0.374170322

Solving
-0.601851852 + x = 0.374170322

Solving for variable 'x'.

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

Add '0.601851852' to each side of the equation.
-0.601851852 + 0.601851852 + x = 0.374170322 + 0.601851852

Combine like terms: -0.601851852 + 0.601851852 = 0.000000000
0.000000000 + x = 0.374170322 + 0.601851852
x = 0.374170322 + 0.601851852

Combine like terms: 0.374170322 + 0.601851852 = 0.976022174
x = 0.976022174

Simplifying
x = 0.976022174

Subproblem 2
x + -0.601851852 = -0.374170322

Simplifying
x + -0.601851852 = -0.374170322

Reorder the terms:
-0.601851852 + x = -0.374170322

Solving
-0.601851852 + x = -0.374170322

Solving for variable 'x'.

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

Add '0.601851852' to each side of the equation.
-0.601851852 + 0.601851852 + x = -0.374170322 + 0.601851852

Combine like terms: -0.601851852 + 0.601851852 = 0.000000000
0.000000000 + x = -0.374170322 + 0.601851852
x = -0.374170322 + 0.601851852

Combine like terms: -0.374170322 + 0.601851852 = 0.22768153
x = 0.22768153

Simplifying
x = 0.22768153

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.976022174, 0.22768153}
Solution
x = {0.976022174, 0.22768153}