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

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

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

Reorder the terms:
5(6 + 2x) = 4(-5 + -2x) * 3x
(6 * 5 + 2x * 5) = 4(-5 + -2x) * 3x
(30 + 10x) = 4(-5 + -2x) * 3x

Reorder the terms for easier multiplication:
30 + 10x = 4 * 3x(-5 + -2x)

Multiply 4 * 3
30 + 10x = 12x(-5 + -2x)
30 + 10x = (-5 * 12x + -2x * 12x)
30 + 10x = (-60x + -24x2)

Solving
30 + 10x = -60x + -24x2

Solving for variable 'x'.

Combine like terms: 10x + 60x = 70x
30 + 70x + 24x2 = -60x + -24x2 + 60x + 24x2

Reorder the terms:
30 + 70x + 24x2 = -60x + 60x + -24x2 + 24x2

Combine like terms: -60x + 60x = 0
30 + 70x + 24x2 = 0 + -24x2 + 24x2
30 + 70x + 24x2 = -24x2 + 24x2

Combine like terms: -24x2 + 24x2 = 0
30 + 70x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 35x + 12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + 35x + 12x2)' equal to zero and attempt to solve:

Simplifying
15 + 35x + 12x2 = 0

Solving
15 + 35x + 12x2 = 0

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

Divide each side by '12'.
1.25 + 2.916666667x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 2.916666667x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 2.916666667x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 2.916666667x + x2 = 0 + -1.25
2.916666667x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
2.916666667x + x2 = -1.25

The x term is 2.916666667x.  Take half its coefficient (1.458333334).
Square it (2.126736113) and add it to both sides.

Add '2.126736113' to each side of the equation.
2.916666667x + 2.126736113 + x2 = -1.25 + 2.126736113

Reorder the terms:
2.126736113 + 2.916666667x + x2 = -1.25 + 2.126736113

Combine like terms: -1.25 + 2.126736113 = 0.876736113
2.126736113 + 2.916666667x + x2 = 0.876736113

Factor a perfect square on the left side:
(x + 1.458333334)(x + 1.458333334) = 0.876736113

Calculate the square root of the right side: 0.936341878

Break this problem into two subproblems by setting 
(x + 1.458333334) equal to 0.936341878 and -0.936341878.

Subproblem 1
x + 1.458333334 = 0.936341878

Simplifying
x + 1.458333334 = 0.936341878

Reorder the terms:
1.458333334 + x = 0.936341878

Solving
1.458333334 + x = 0.936341878

Solving for variable 'x'.

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

Add '-1.458333334' to each side of the equation.
1.458333334 + -1.458333334 + x = 0.936341878 + -1.458333334

Combine like terms: 1.458333334 + -1.458333334 = 0.000000000
0.000000000 + x = 0.936341878 + -1.458333334
x = 0.936341878 + -1.458333334

Combine like terms: 0.936341878 + -1.458333334 = -0.521991456
x = -0.521991456

Simplifying
x = -0.521991456

Subproblem 2
x + 1.458333334 = -0.936341878

Simplifying
x + 1.458333334 = -0.936341878

Reorder the terms:
1.458333334 + x = -0.936341878

Solving
1.458333334 + x = -0.936341878

Solving for variable 'x'.

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

Add '-1.458333334' to each side of the equation.
1.458333334 + -1.458333334 + x = -0.936341878 + -1.458333334

Combine like terms: 1.458333334 + -1.458333334 = 0.000000000
0.000000000 + x = -0.936341878 + -1.458333334
x = -0.936341878 + -1.458333334

Combine like terms: -0.936341878 + -1.458333334 = -2.394675212
x = -2.394675212

Simplifying
x = -2.394675212

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.521991456, -2.394675212}
Solution
x = {-0.521991456, -2.394675212}