15(2x+6)+3(x-4)(x+4)=3x+2-5(4x+2)

Solution for 15(2x+6)+3(x-4)(x+4)=3x+2-5(4x+2) equation:

Simplifying
15(2x + 6) + 3(x + -4)(x + 4) = 3x + 2 + -5(4x + 2)

Reorder the terms:
15(6 + 2x) + 3(x + -4)(x + 4) = 3x + 2 + -5(4x + 2)
(6 * 15 + 2x * 15) + 3(x + -4)(x + 4) = 3x + 2 + -5(4x + 2)
(90 + 30x) + 3(x + -4)(x + 4) = 3x + 2 + -5(4x + 2)

Reorder the terms:
90 + 30x + 3(-4 + x)(x + 4) = 3x + 2 + -5(4x + 2)

Reorder the terms:
90 + 30x + 3(-4 + x)(4 + x) = 3x + 2 + -5(4x + 2)

Multiply (-4 + x) * (4 + x)
90 + 30x + 3(-4(4 + x) + x(4 + x)) = 3x + 2 + -5(4x + 2)
90 + 30x + 3((4 * -4 + x * -4) + x(4 + x)) = 3x + 2 + -5(4x + 2)
90 + 30x + 3((-16 + -4x) + x(4 + x)) = 3x + 2 + -5(4x + 2)
90 + 30x + 3(-16 + -4x + (4 * x + x * x)) = 3x + 2 + -5(4x + 2)
90 + 30x + 3(-16 + -4x + (4x + x2)) = 3x + 2 + -5(4x + 2)

Combine like terms: -4x + 4x = 0
90 + 30x + 3(-16 + 0 + x2) = 3x + 2 + -5(4x + 2)
90 + 30x + 3(-16 + x2) = 3x + 2 + -5(4x + 2)
90 + 30x + (-16 * 3 + x2 * 3) = 3x + 2 + -5(4x + 2)
90 + 30x + (-48 + 3x2) = 3x + 2 + -5(4x + 2)

Reorder the terms:
90 + -48 + 30x + 3x2 = 3x + 2 + -5(4x + 2)

Combine like terms: 90 + -48 = 42
42 + 30x + 3x2 = 3x + 2 + -5(4x + 2)

Reorder the terms:
42 + 30x + 3x2 = 3x + 2 + -5(2 + 4x)
42 + 30x + 3x2 = 3x + 2 + (2 * -5 + 4x * -5)
42 + 30x + 3x2 = 3x + 2 + (-10 + -20x)

Reorder the terms:
42 + 30x + 3x2 = 2 + -10 + 3x + -20x

Combine like terms: 2 + -10 = -8
42 + 30x + 3x2 = -8 + 3x + -20x

Combine like terms: 3x + -20x = -17x
42 + 30x + 3x2 = -8 + -17x

Solving
42 + 30x + 3x2 = -8 + -17x

Solving for variable 'x'.

Reorder the terms:
42 + 8 + 30x + 17x + 3x2 = -8 + -17x + 8 + 17x

Combine like terms: 42 + 8 = 50
50 + 30x + 17x + 3x2 = -8 + -17x + 8 + 17x

Combine like terms: 30x + 17x = 47x
50 + 47x + 3x2 = -8 + -17x + 8 + 17x

Reorder the terms:
50 + 47x + 3x2 = -8 + 8 + -17x + 17x

Combine like terms: -8 + 8 = 0
50 + 47x + 3x2 = 0 + -17x + 17x
50 + 47x + 3x2 = -17x + 17x

Combine like terms: -17x + 17x = 0
50 + 47x + 3x2 = 0

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

Divide each side by '3'.
16.66666667 + 15.66666667x + x2 = 0

Move the constant term to the right:

Add '-16.66666667' to each side of the equation.
16.66666667 + 15.66666667x + -16.66666667 + x2 = 0 + -16.66666667

Reorder the terms:
16.66666667 + -16.66666667 + 15.66666667x + x2 = 0 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + 15.66666667x + x2 = 0 + -16.66666667
15.66666667x + x2 = 0 + -16.66666667

Combine like terms: 0 + -16.66666667 = -16.66666667
15.66666667x + x2 = -16.66666667

The x term is 15.66666667x.  Take half its coefficient (7.833333335).
Square it (61.36111114) and add it to both sides.

Add '61.36111114' to each side of the equation.
15.66666667x + 61.36111114 + x2 = -16.66666667 + 61.36111114

Reorder the terms:
61.36111114 + 15.66666667x + x2 = -16.66666667 + 61.36111114

Combine like terms: -16.66666667 + 61.36111114 = 44.69444447
61.36111114 + 15.66666667x + x2 = 44.69444447

Factor a perfect square on the left side:
(x + 7.833333335)(x + 7.833333335) = 44.69444447

Calculate the square root of the right side: 6.685390375

Break this problem into two subproblems by setting 
(x + 7.833333335) equal to 6.685390375 and -6.685390375.

Subproblem 1
x + 7.833333335 = 6.685390375

Simplifying
x + 7.833333335 = 6.685390375

Reorder the terms:
7.833333335 + x = 6.685390375

Solving
7.833333335 + x = 6.685390375

Solving for variable 'x'.

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

Add '-7.833333335' to each side of the equation.
7.833333335 + -7.833333335 + x = 6.685390375 + -7.833333335

Combine like terms: 7.833333335 + -7.833333335 = 0.000000000
0.000000000 + x = 6.685390375 + -7.833333335
x = 6.685390375 + -7.833333335

Combine like terms: 6.685390375 + -7.833333335 = -1.14794296
x = -1.14794296

Simplifying
x = -1.14794296

Subproblem 2
x + 7.833333335 = -6.685390375

Simplifying
x + 7.833333335 = -6.685390375

Reorder the terms:
7.833333335 + x = -6.685390375

Solving
7.833333335 + x = -6.685390375

Solving for variable 'x'.

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

Add '-7.833333335' to each side of the equation.
7.833333335 + -7.833333335 + x = -6.685390375 + -7.833333335

Combine like terms: 7.833333335 + -7.833333335 = 0.000000000
0.000000000 + x = -6.685390375 + -7.833333335
x = -6.685390375 + -7.833333335

Combine like terms: -6.685390375 + -7.833333335 = -14.51872371
x = -14.51872371

Simplifying
x = -14.51872371

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.14794296, -14.51872371}