3x-4(8x+2)=(5x+2)(3x+4)-15x

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Solution for 3x-4(8x+2)=(5x+2)(3x+4)-15x equation: 


Simplifying
3x + -4(8x + 2) = (5x + 2)(3x + 4) + -15x

Reorder the terms:
3x + -4(2 + 8x) = (5x + 2)(3x + 4) + -15x
3x + (2 * -4 + 8x * -4) = (5x + 2)(3x + 4) + -15x
3x + (-8 + -32x) = (5x + 2)(3x + 4) + -15x

Reorder the terms:
-8 + 3x + -32x = (5x + 2)(3x + 4) + -15x

Combine like terms: 3x + -32x = -29x
-8 + -29x = (5x + 2)(3x + 4) + -15x

Reorder the terms:
-8 + -29x = (2 + 5x)(3x + 4) + -15x

Reorder the terms:
-8 + -29x = (2 + 5x)(4 + 3x) + -15x

Multiply (2 + 5x) * (4 + 3x)
-8 + -29x = (2(4 + 3x) + 5x * (4 + 3x)) + -15x
-8 + -29x = ((4 * 2 + 3x * 2) + 5x * (4 + 3x)) + -15x
-8 + -29x = ((8 + 6x) + 5x * (4 + 3x)) + -15x
-8 + -29x = (8 + 6x + (4 * 5x + 3x * 5x)) + -15x
-8 + -29x = (8 + 6x + (20x + 15x2)) + -15x

Combine like terms: 6x + 20x = 26x
-8 + -29x = (8 + 26x + 15x2) + -15x

Reorder the terms:
-8 + -29x = 8 + 26x + -15x + 15x2

Combine like terms: 26x + -15x = 11x
-8 + -29x = 8 + 11x + 15x2

Solving
-8 + -29x = 8 + 11x + 15x2

Solving for variable 'x'.

Reorder the terms:
-8 + -8 + -29x + -11x + -15x2 = 8 + 11x + 15x2 + -8 + -11x + -15x2

Combine like terms: -8 + -8 = -16
-16 + -29x + -11x + -15x2 = 8 + 11x + 15x2 + -8 + -11x + -15x2

Combine like terms: -29x + -11x = -40x
-16 + -40x + -15x2 = 8 + 11x + 15x2 + -8 + -11x + -15x2

Reorder the terms:
-16 + -40x + -15x2 = 8 + -8 + 11x + -11x + 15x2 + -15x2

Combine like terms: 8 + -8 = 0
-16 + -40x + -15x2 = 0 + 11x + -11x + 15x2 + -15x2
-16 + -40x + -15x2 = 11x + -11x + 15x2 + -15x2

Combine like terms: 11x + -11x = 0
-16 + -40x + -15x2 = 0 + 15x2 + -15x2
-16 + -40x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-16 + -40x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 40x + 15x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(16 + 40x + 15x2)' equal to zero and attempt to solve:

Simplifying
16 + 40x + 15x2 = 0

Solving
16 + 40x + 15x2 = 0

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

Divide each side by '15'.
1.066666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.066666667' to each side of the equation.
1.066666667 + 2.666666667x + -1.066666667 + x2 = 0 + -1.066666667

Reorder the terms:
1.066666667 + -1.066666667 + 2.666666667x + x2 = 0 + -1.066666667

Combine like terms: 1.066666667 + -1.066666667 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + -1.066666667
2.666666667x + x2 = 0 + -1.066666667

Combine like terms: 0 + -1.066666667 = -1.066666667
2.666666667x + x2 = -1.066666667

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 = -1.066666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -1.066666667 + 1.777777780

Combine like terms: -1.066666667 + 1.777777780 = 0.711111113
1.777777780 + 2.666666667x + x2 = 0.711111113

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 0.711111113

Calculate the square root of the right side: 0.843274044

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 0.843274044 and -0.843274044.


Subproblem 1
x + 1.333333334 = 0.843274044

Simplifying
x + 1.333333334 = 0.843274044

Reorder the terms:
1.333333334 + x = 0.843274044

Solving
1.333333334 + x = 0.843274044

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 = 0.843274044 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 0.843274044 + -1.333333334
x = 0.843274044 + -1.333333334

Combine like terms: 0.843274044 + -1.333333334 = -0.49005929
x = -0.49005929

Simplifying
x = -0.49005929


Subproblem 2
x + 1.333333334 = -0.843274044

Simplifying
x + 1.333333334 = -0.843274044

Reorder the terms:
1.333333334 + x = -0.843274044

Solving
1.333333334 + x = -0.843274044

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 = -0.843274044 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -0.843274044 + -1.333333334
x = -0.843274044 + -1.333333334

Combine like terms: -0.843274044 + -1.333333334 = -2.176607378
x = -2.176607378

Simplifying
x = -2.176607378


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.49005929, -2.176607378}
Solution
x = {-0.49005929, -2.176607378}

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