9(3x-4)=5(x-4)22x

Solution for 9(3x-4)=5(x-4)22x equation:

Simplifying
9(3x + -4) = 5(x + -4) * 22x

Reorder the terms:
9(-4 + 3x) = 5(x + -4) * 22x
(-4 * 9 + 3x * 9) = 5(x + -4) * 22x
(-36 + 27x) = 5(x + -4) * 22x

Reorder the terms:
-36 + 27x = 5(-4 + x) * 22x

Reorder the terms for easier multiplication:
-36 + 27x = 5 * 22x(-4 + x)

Multiply 5 * 22
-36 + 27x = 110x(-4 + x)
-36 + 27x = (-4 * 110x + x * 110x)
-36 + 27x = (-440x + 110x2)

Solving
-36 + 27x = -440x + 110x2

Solving for variable 'x'.

Combine like terms: 27x + 440x = 467x
-36 + 467x + -110x2 = -440x + 110x2 + 440x + -110x2

Reorder the terms:
-36 + 467x + -110x2 = -440x + 440x + 110x2 + -110x2

Combine like terms: -440x + 440x = 0
-36 + 467x + -110x2 = 0 + 110x2 + -110x2
-36 + 467x + -110x2 = 110x2 + -110x2

Combine like terms: 110x2 + -110x2 = 0
-36 + 467x + -110x2 = 0

Begin completing the square.  Divide all terms by
-110 the coefficient of the squared term: 

Divide each side by '-110'.
0.3272727273 + -4.245454545x + x2 = 0

Move the constant term to the right:

Add '-0.3272727273' to each side of the equation.
0.3272727273 + -4.245454545x + -0.3272727273 + x2 = 0 + -0.3272727273

Reorder the terms:
0.3272727273 + -0.3272727273 + -4.245454545x + x2 = 0 + -0.3272727273

Combine like terms: 0.3272727273 + -0.3272727273 = 0.0000000000
0.0000000000 + -4.245454545x + x2 = 0 + -0.3272727273
-4.245454545x + x2 = 0 + -0.3272727273

Combine like terms: 0 + -0.3272727273 = -0.3272727273
-4.245454545x + x2 = -0.3272727273

The x term is -4.245454545x.  Take half its coefficient (-2.122727273).
Square it (4.505971076) and add it to both sides.

Add '4.505971076' to each side of the equation.
-4.245454545x + 4.505971076 + x2 = -0.3272727273 + 4.505971076

Reorder the terms:
4.505971076 + -4.245454545x + x2 = -0.3272727273 + 4.505971076

Combine like terms: -0.3272727273 + 4.505971076 = 4.1786983487
4.505971076 + -4.245454545x + x2 = 4.1786983487

Factor a perfect square on the left side:
(x + -2.122727273)(x + -2.122727273) = 4.1786983487

Calculate the square root of the right side: 2.044186476

Break this problem into two subproblems by setting 
(x + -2.122727273) equal to 2.044186476 and -2.044186476.

Subproblem 1
x + -2.122727273 = 2.044186476

Simplifying
x + -2.122727273 = 2.044186476

Reorder the terms:
-2.122727273 + x = 2.044186476

Solving
-2.122727273 + x = 2.044186476

Solving for variable 'x'.

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

Add '2.122727273' to each side of the equation.
-2.122727273 + 2.122727273 + x = 2.044186476 + 2.122727273

Combine like terms: -2.122727273 + 2.122727273 = 0.000000000
0.000000000 + x = 2.044186476 + 2.122727273
x = 2.044186476 + 2.122727273

Combine like terms: 2.044186476 + 2.122727273 = 4.166913749
x = 4.166913749

Simplifying
x = 4.166913749

Subproblem 2
x + -2.122727273 = -2.044186476

Simplifying
x + -2.122727273 = -2.044186476

Reorder the terms:
-2.122727273 + x = -2.044186476

Solving
-2.122727273 + x = -2.044186476

Solving for variable 'x'.

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

Add '2.122727273' to each side of the equation.
-2.122727273 + 2.122727273 + x = -2.044186476 + 2.122727273

Combine like terms: -2.122727273 + 2.122727273 = 0.000000000
0.000000000 + x = -2.044186476 + 2.122727273
x = -2.044186476 + 2.122727273

Combine like terms: -2.044186476 + 2.122727273 = 0.078540797
x = 0.078540797

Simplifying
x = 0.078540797

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.166913749, 0.078540797}