3(x-2)5(2x-3)=23

Solution for 3(x-2)5(2x-3)=23 equation:

Simplifying
3(x + -2) * 5(2x + -3) = 23

Reorder the terms:
3(-2 + x) * 5(2x + -3) = 23

Reorder the terms:
3(-2 + x) * 5(-3 + 2x) = 23

Reorder the terms for easier multiplication:
3 * 5(-2 + x)(-3 + 2x) = 23

Multiply 3 * 5
15(-2 + x)(-3 + 2x) = 23

Multiply (-2 + x) * (-3 + 2x)
15(-2(-3 + 2x) + x(-3 + 2x)) = 23
15((-3 * -2 + 2x * -2) + x(-3 + 2x)) = 23
15((6 + -4x) + x(-3 + 2x)) = 23
15(6 + -4x + (-3 * x + 2x * x)) = 23
15(6 + -4x + (-3x + 2x2)) = 23

Combine like terms: -4x + -3x = -7x
15(6 + -7x + 2x2) = 23
(6 * 15 + -7x * 15 + 2x2 * 15) = 23
(90 + -105x + 30x2) = 23

Solving
90 + -105x + 30x2 = 23

Solving for variable 'x'.

Reorder the terms:
90 + -23 + -105x + 30x2 = 23 + -23

Combine like terms: 90 + -23 = 67
67 + -105x + 30x2 = 23 + -23

Combine like terms: 23 + -23 = 0
67 + -105x + 30x2 = 0

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

Divide each side by '30'.
2.233333333 + -3.5x + x2 = 0.0

Move the constant term to the right:

Add '-2.233333333' to each side of the equation.
2.233333333 + -3.5x + -2.233333333 + x2 = 0.0 + -2.233333333

Reorder the terms:
2.233333333 + -2.233333333 + -3.5x + x2 = 0.0 + -2.233333333

Combine like terms: 2.233333333 + -2.233333333 = 0.000000000
0.000000000 + -3.5x + x2 = 0.0 + -2.233333333
-3.5x + x2 = 0.0 + -2.233333333

Combine like terms: 0.0 + -2.233333333 = -2.233333333
-3.5x + x2 = -2.233333333

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -2.233333333 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -2.233333333 + 3.0625

Combine like terms: -2.233333333 + 3.0625 = 0.829166667
3.0625 + -3.5x + x2 = 0.829166667

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 0.829166667

Calculate the square root of the right side: 0.910585892

Break this problem into two subproblems by setting 
(x + -1.75) equal to 0.910585892 and -0.910585892.

Subproblem 1
x + -1.75 = 0.910585892

Simplifying
x + -1.75 = 0.910585892

Reorder the terms:
-1.75 + x = 0.910585892

Solving
-1.75 + x = 0.910585892

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 0.910585892 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 0.910585892 + 1.75
x = 0.910585892 + 1.75

Combine like terms: 0.910585892 + 1.75 = 2.660585892
x = 2.660585892

Simplifying
x = 2.660585892

Subproblem 2
x + -1.75 = -0.910585892

Simplifying
x + -1.75 = -0.910585892

Reorder the terms:
-1.75 + x = -0.910585892

Solving
-1.75 + x = -0.910585892

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -0.910585892 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -0.910585892 + 1.75
x = -0.910585892 + 1.75

Combine like terms: -0.910585892 + 1.75 = 0.839414108
x = 0.839414108

Simplifying
x = 0.839414108

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.660585892, 0.839414108}