5(3x-1)3(2x-1)=22

Solution for 5(3x-1)3(2x-1)=22 equation:

Simplifying
5(3x + -1) * 3(2x + -1) = 22

Reorder the terms:
5(-1 + 3x) * 3(2x + -1) = 22

Reorder the terms:
5(-1 + 3x) * 3(-1 + 2x) = 22

Reorder the terms for easier multiplication:
5 * 3(-1 + 3x)(-1 + 2x) = 22

Multiply 5 * 3
15(-1 + 3x)(-1 + 2x) = 22

Multiply (-1 + 3x) * (-1 + 2x)
15(-1(-1 + 2x) + 3x * (-1 + 2x)) = 22
15((-1 * -1 + 2x * -1) + 3x * (-1 + 2x)) = 22
15((1 + -2x) + 3x * (-1 + 2x)) = 22
15(1 + -2x + (-1 * 3x + 2x * 3x)) = 22
15(1 + -2x + (-3x + 6x2)) = 22

Combine like terms: -2x + -3x = -5x
15(1 + -5x + 6x2) = 22
(1 * 15 + -5x * 15 + 6x2 * 15) = 22
(15 + -75x + 90x2) = 22

Solving
15 + -75x + 90x2 = 22

Solving for variable 'x'.

Reorder the terms:
15 + -22 + -75x + 90x2 = 22 + -22

Combine like terms: 15 + -22 = -7
-7 + -75x + 90x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-7 + -75x + 90x2 = 0

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

Divide each side by '90'.
-0.07777777778 + -0.8333333333x + x2 = 0.0

Move the constant term to the right:

Add '0.07777777778' to each side of the equation.
-0.07777777778 + -0.8333333333x + 0.07777777778 + x2 = 0.0 + 0.07777777778

Reorder the terms:
-0.07777777778 + 0.07777777778 + -0.8333333333x + x2 = 0.0 + 0.07777777778

Combine like terms: -0.07777777778 + 0.07777777778 = 0.00000000000
0.00000000000 + -0.8333333333x + x2 = 0.0 + 0.07777777778
-0.8333333333x + x2 = 0.0 + 0.07777777778

Combine like terms: 0.0 + 0.07777777778 = 0.07777777778
-0.8333333333x + x2 = 0.07777777778

The x term is -0.8333333333x.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333x + 0.1736111111 + x2 = 0.07777777778 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = 0.07777777778 + 0.1736111111

Combine like terms: 0.07777777778 + 0.1736111111 = 0.25138888888
0.1736111111 + -0.8333333333x + x2 = 0.25138888888

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 0.25138888888

Calculate the square root of the right side: 0.501386965

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 0.501386965 and -0.501386965.

Subproblem 1
x + -0.4166666667 = 0.501386965

Simplifying
x + -0.4166666667 = 0.501386965

Reorder the terms:
-0.4166666667 + x = 0.501386965

Solving
-0.4166666667 + x = 0.501386965

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = 0.501386965 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = 0.501386965 + 0.4166666667
x = 0.501386965 + 0.4166666667

Combine like terms: 0.501386965 + 0.4166666667 = 0.9180536317
x = 0.9180536317

Simplifying
x = 0.9180536317

Subproblem 2
x + -0.4166666667 = -0.501386965

Simplifying
x + -0.4166666667 = -0.501386965

Reorder the terms:
-0.4166666667 + x = -0.501386965

Solving
-0.4166666667 + x = -0.501386965

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = -0.501386965 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = -0.501386965 + 0.4166666667
x = -0.501386965 + 0.4166666667

Combine like terms: -0.501386965 + 0.4166666667 = -0.0847202983
x = -0.0847202983

Simplifying
x = -0.0847202983

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9180536317, -0.0847202983}