3(x-5+2)(3x+1)=45

Solution for 3(x-5+2)(3x+1)=45 equation:

Simplifying
3(x + -5 + 2)(3x + 1) = 45

Reorder the terms:
3(-5 + 2 + x)(3x + 1) = 45

Combine like terms: -5 + 2 = -3
3(-3 + x)(3x + 1) = 45

Reorder the terms:
3(-3 + x)(1 + 3x) = 45

Multiply (-3 + x) * (1 + 3x)
3(-3(1 + 3x) + x(1 + 3x)) = 45
3((1 * -3 + 3x * -3) + x(1 + 3x)) = 45
3((-3 + -9x) + x(1 + 3x)) = 45
3(-3 + -9x + (1 * x + 3x * x)) = 45
3(-3 + -9x + (1x + 3x2)) = 45

Combine like terms: -9x + 1x = -8x
3(-3 + -8x + 3x2) = 45
(-3 * 3 + -8x * 3 + 3x2 * 3) = 45
(-9 + -24x + 9x2) = 45

Solving
-9 + -24x + 9x2 = 45

Solving for variable 'x'.

Reorder the terms:
-9 + -45 + -24x + 9x2 = 45 + -45

Combine like terms: -9 + -45 = -54
-54 + -24x + 9x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-54 + -24x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -8x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-18 + -8x + 3x2)' equal to zero and attempt to solve:

Simplifying
-18 + -8x + 3x2 = 0

Solving
-18 + -8x + 3x2 = 0

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

Divide each side by '3'.
-6 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2.666666667x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -2.666666667x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2.666666667x + x2 = 0 + 6
-2.666666667x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2.666666667x + x2 = 6

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 6 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 6 + 1.777777780

Combine like terms: 6 + 1.777777780 = 7.77777778
1.777777780 + -2.666666667x + x2 = 7.77777778

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 7.77777778

Calculate the square root of the right side: 2.788866756

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 2.788866756 and -2.788866756.

Subproblem 1
x + -1.333333334 = 2.788866756

Simplifying
x + -1.333333334 = 2.788866756

Reorder the terms:
-1.333333334 + x = 2.788866756

Solving
-1.333333334 + x = 2.788866756

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 2.788866756 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 2.788866756 + 1.333333334
x = 2.788866756 + 1.333333334

Combine like terms: 2.788866756 + 1.333333334 = 4.12220009
x = 4.12220009

Simplifying
x = 4.12220009

Subproblem 2
x + -1.333333334 = -2.788866756

Simplifying
x + -1.333333334 = -2.788866756

Reorder the terms:
-1.333333334 + x = -2.788866756

Solving
-1.333333334 + x = -2.788866756

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -2.788866756 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -2.788866756 + 1.333333334
x = -2.788866756 + 1.333333334

Combine like terms: -2.788866756 + 1.333333334 = -1.455533422
x = -1.455533422

Simplifying
x = -1.455533422

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.12220009, -1.455533422}
Solution
x = {4.12220009, -1.455533422}