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 = -50x
30 + -50x + -24x2 = 60x + 24x2 + -60x + -24x2

Reorder the terms:
30 + -50x + -24x2 = 60x + -60x + 24x2 + -24x2

Combine like terms: 60x + -60x = 0
30 + -50x + -24x2 = 0 + 24x2 + -24x2
30 + -50x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
30 + -50x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -25x + -12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + -25x + -12x2)' equal to zero and attempt to solve:

Simplifying
15 + -25x + -12x2 = 0

Solving
15 + -25x + -12x2 = 0

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

Divide each side by '-12'.
-1.25 + 2.083333333x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2.083333333x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2.083333333x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2.083333333x + x2 = 0 + 1.25
2.083333333x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
2.083333333x + x2 = 1.25

The x term is 2.083333333x.  Take half its coefficient (1.041666667).
Square it (1.085069445) and add it to both sides.

Add '1.085069445' to each side of the equation.
2.083333333x + 1.085069445 + x2 = 1.25 + 1.085069445

Reorder the terms:
1.085069445 + 2.083333333x + x2 = 1.25 + 1.085069445

Combine like terms: 1.25 + 1.085069445 = 2.335069445
1.085069445 + 2.083333333x + x2 = 2.335069445

Factor a perfect square on the left side:
(x + 1.041666667)(x + 1.041666667) = 2.335069445

Calculate the square root of the right side: 1.528093402

Break this problem into two subproblems by setting 
(x + 1.041666667) equal to 1.528093402 and -1.528093402.

Subproblem 1
x + 1.041666667 = 1.528093402

Simplifying
x + 1.041666667 = 1.528093402

Reorder the terms:
1.041666667 + x = 1.528093402

Solving
1.041666667 + x = 1.528093402

Solving for variable 'x'.

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

Add '-1.041666667' to each side of the equation.
1.041666667 + -1.041666667 + x = 1.528093402 + -1.041666667

Combine like terms: 1.041666667 + -1.041666667 = 0.000000000
0.000000000 + x = 1.528093402 + -1.041666667
x = 1.528093402 + -1.041666667

Combine like terms: 1.528093402 + -1.041666667 = 0.486426735
x = 0.486426735

Simplifying
x = 0.486426735

Subproblem 2
x + 1.041666667 = -1.528093402

Simplifying
x + 1.041666667 = -1.528093402

Reorder the terms:
1.041666667 + x = -1.528093402

Solving
1.041666667 + x = -1.528093402

Solving for variable 'x'.

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

Add '-1.041666667' to each side of the equation.
1.041666667 + -1.041666667 + x = -1.528093402 + -1.041666667

Combine like terms: 1.041666667 + -1.041666667 = 0.000000000
0.000000000 + x = -1.528093402 + -1.041666667
x = -1.528093402 + -1.041666667

Combine like terms: -1.528093402 + -1.041666667 = -2.569760069
x = -2.569760069

Simplifying
x = -2.569760069

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.486426735, -2.569760069}
Solution
x = {0.486426735, -2.569760069}