(x+3)2(2-3x)=5(x+4)-1

Solution for (x+3)2(2-3x)=5(x+4)-1 equation:

Simplifying
(x + 3) * 2(2 + -3x) = 5(x + 4) + -1

Reorder the terms:
(3 + x) * 2(2 + -3x) = 5(x + 4) + -1

Reorder the terms for easier multiplication:
2(3 + x)(2 + -3x) = 5(x + 4) + -1

Multiply (3 + x) * (2 + -3x)
2(3(2 + -3x) + x(2 + -3x)) = 5(x + 4) + -1
2((2 * 3 + -3x * 3) + x(2 + -3x)) = 5(x + 4) + -1
2((6 + -9x) + x(2 + -3x)) = 5(x + 4) + -1
2(6 + -9x + (2 * x + -3x * x)) = 5(x + 4) + -1
2(6 + -9x + (2x + -3x2)) = 5(x + 4) + -1

Combine like terms: -9x + 2x = -7x
2(6 + -7x + -3x2) = 5(x + 4) + -1
(6 * 2 + -7x * 2 + -3x2 * 2) = 5(x + 4) + -1
(12 + -14x + -6x2) = 5(x + 4) + -1

Reorder the terms:
12 + -14x + -6x2 = 5(4 + x) + -1
12 + -14x + -6x2 = (4 * 5 + x * 5) + -1
12 + -14x + -6x2 = (20 + 5x) + -1

Reorder the terms:
12 + -14x + -6x2 = 20 + -1 + 5x

Combine like terms: 20 + -1 = 19
12 + -14x + -6x2 = 19 + 5x

Solving
12 + -14x + -6x2 = 19 + 5x

Solving for variable 'x'.

Reorder the terms:
12 + -19 + -14x + -5x + -6x2 = 19 + 5x + -19 + -5x

Combine like terms: 12 + -19 = -7
-7 + -14x + -5x + -6x2 = 19 + 5x + -19 + -5x

Combine like terms: -14x + -5x = -19x
-7 + -19x + -6x2 = 19 + 5x + -19 + -5x

Reorder the terms:
-7 + -19x + -6x2 = 19 + -19 + 5x + -5x

Combine like terms: 19 + -19 = 0
-7 + -19x + -6x2 = 0 + 5x + -5x
-7 + -19x + -6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-7 + -19x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 19x + 6x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 19x + 6x2)' equal to zero and attempt to solve:

Simplifying
7 + 19x + 6x2 = 0

Solving
7 + 19x + 6x2 = 0

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

Divide each side by '6'.
1.166666667 + 3.166666667x + x2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + 3.166666667x + -1.166666667 + x2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + 3.166666667x + x2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + 3.166666667x + x2 = 0 + -1.166666667
3.166666667x + x2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
3.166666667x + x2 = -1.166666667

The x term is 3.166666667x.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667x + 2.506944447 + x2 = -1.166666667 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667x + x2 = -1.166666667 + 2.506944447

Combine like terms: -1.166666667 + 2.506944447 = 1.34027778
2.506944447 + 3.166666667x + x2 = 1.34027778

Factor a perfect square on the left side:
(x + 1.583333334)(x + 1.583333334) = 1.34027778

Calculate the square root of the right side: 1.157703667

Break this problem into two subproblems by setting 
(x + 1.583333334) equal to 1.157703667 and -1.157703667.

Subproblem 1
x + 1.583333334 = 1.157703667

Simplifying
x + 1.583333334 = 1.157703667

Reorder the terms:
1.583333334 + x = 1.157703667

Solving
1.583333334 + x = 1.157703667

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = 1.157703667 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = 1.157703667 + -1.583333334
x = 1.157703667 + -1.583333334

Combine like terms: 1.157703667 + -1.583333334 = -0.425629667
x = -0.425629667

Simplifying
x = -0.425629667

Subproblem 2
x + 1.583333334 = -1.157703667

Simplifying
x + 1.583333334 = -1.157703667

Reorder the terms:
1.583333334 + x = -1.157703667

Solving
1.583333334 + x = -1.157703667

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = -1.157703667 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = -1.157703667 + -1.583333334
x = -1.157703667 + -1.583333334

Combine like terms: -1.157703667 + -1.583333334 = -2.741037001
x = -2.741037001

Simplifying
x = -2.741037001

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.425629667, -2.741037001}
Solution
x = {-0.425629667, -2.741037001}