(x-3)*3(x+1)=3(2x-1)

Solution for (x-3)*3(x+1)=3(2x-1) equation:

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

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

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

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

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

Combine like terms: -3x + 1x = -2x
3(-3 + -2x + x2) = 3(2x + -1)
(-3 * 3 + -2x * 3 + x2 * 3) = 3(2x + -1)
(-9 + -6x + 3x2) = 3(2x + -1)

Reorder the terms:
-9 + -6x + 3x2 = 3(-1 + 2x)
-9 + -6x + 3x2 = (-1 * 3 + 2x * 3)
-9 + -6x + 3x2 = (-3 + 6x)

Solving
-9 + -6x + 3x2 = -3 + 6x

Solving for variable 'x'.

Reorder the terms:
-9 + 3 + -6x + -6x + 3x2 = -3 + 6x + 3 + -6x

Combine like terms: -9 + 3 = -6
-6 + -6x + -6x + 3x2 = -3 + 6x + 3 + -6x

Combine like terms: -6x + -6x = -12x
-6 + -12x + 3x2 = -3 + 6x + 3 + -6x

Reorder the terms:
-6 + -12x + 3x2 = -3 + 3 + 6x + -6x

Combine like terms: -3 + 3 = 0
-6 + -12x + 3x2 = 0 + 6x + -6x
-6 + -12x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6 + -12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -4x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -4x + x2 = 0

Solving
-2 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -4x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4x + x2 = 0 + 2
-4x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4x + x2 = 2

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 2 + 4

Reorder the terms:
4 + -4x + x2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + -4x + x2 = 6

Factor a perfect square on the left side:
(x + -2)(x + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -2) equal to 2.449489743 and -2.449489743.

Subproblem 1
x + -2 = 2.449489743

Simplifying
x + -2 = 2.449489743

Reorder the terms:
-2 + x = 2.449489743

Solving
-2 + x = 2.449489743

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.449489743 + 2
x = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
x = 4.449489743

Simplifying
x = 4.449489743

Subproblem 2
x + -2 = -2.449489743

Simplifying
x + -2 = -2.449489743

Reorder the terms:
-2 + x = -2.449489743

Solving
-2 + x = -2.449489743

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.449489743 + 2
x = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
x = -0.449489743

Simplifying
x = -0.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.449489743, -0.449489743}
Solution
x = {4.449489743, -0.449489743}