-2x(x+2-3x-5)=30(3x-4+6-2x)

Solution for -2x(x+2-3x-5)=30(3x-4+6-2x) equation:

Simplifying
-2x(x + 2 + -3x + -5) = 30(3x + -4 + 6 + -2x)

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

Combine like terms: 2 + -5 = -3
-2x(-3 + x + -3x) = 30(3x + -4 + 6 + -2x)

Combine like terms: x + -3x = -2x
-2x(-3 + -2x) = 30(3x + -4 + 6 + -2x)
(-3 * -2x + -2x * -2x) = 30(3x + -4 + 6 + -2x)
(6x + 4x2) = 30(3x + -4 + 6 + -2x)

Reorder the terms:
6x + 4x2 = 30(-4 + 6 + 3x + -2x)

Combine like terms: -4 + 6 = 2
6x + 4x2 = 30(2 + 3x + -2x)

Combine like terms: 3x + -2x = 1x
6x + 4x2 = 30(2 + 1x)
6x + 4x2 = (2 * 30 + 1x * 30)
6x + 4x2 = (60 + 30x)

Solving
6x + 4x2 = 60 + 30x

Solving for variable 'x'.

Reorder the terms:
-60 + 6x + -30x + 4x2 = 60 + 30x + -60 + -30x

Combine like terms: 6x + -30x = -24x
-60 + -24x + 4x2 = 60 + 30x + -60 + -30x

Reorder the terms:
-60 + -24x + 4x2 = 60 + -60 + 30x + -30x

Combine like terms: 60 + -60 = 0
-60 + -24x + 4x2 = 0 + 30x + -30x
-60 + -24x + 4x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
-60 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -6x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-15 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + -6x + x2 = 0

Solving
-15 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -6x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -6x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -6x + x2 = 0 + 15
-6x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-6x + x2 = 15

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 15 + 9

Reorder the terms:
9 + -6x + x2 = 15 + 9

Combine like terms: 15 + 9 = 24
9 + -6x + x2 = 24

Factor a perfect square on the left side:
(x + -3)(x + -3) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -3) equal to 4.898979486 and -4.898979486.

Subproblem 1
x + -3 = 4.898979486

Simplifying
x + -3 = 4.898979486

Reorder the terms:
-3 + x = 4.898979486

Solving
-3 + x = 4.898979486

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 4.898979486 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.898979486 + 3
x = 4.898979486 + 3

Combine like terms: 4.898979486 + 3 = 7.898979486
x = 7.898979486

Simplifying
x = 7.898979486

Subproblem 2
x + -3 = -4.898979486

Simplifying
x + -3 = -4.898979486

Reorder the terms:
-3 + x = -4.898979486

Solving
-3 + x = -4.898979486

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -4.898979486 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.898979486 + 3
x = -4.898979486 + 3

Combine like terms: -4.898979486 + 3 = -1.898979486
x = -1.898979486

Simplifying
x = -1.898979486

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.898979486, -1.898979486}
Solution
x = {7.898979486, -1.898979486}