2(x-1)(x+5)=2-x(2x+16)

Solution for 2(x-1)(x+5)=2-x(2x+16) equation:

Simplifying
2(x + -1)(x + 5) = 2 + -1x(2x + 16)

Reorder the terms:
2(-1 + x)(x + 5) = 2 + -1x(2x + 16)

Reorder the terms:
2(-1 + x)(5 + x) = 2 + -1x(2x + 16)

Multiply (-1 + x) * (5 + x)
2(-1(5 + x) + x(5 + x)) = 2 + -1x(2x + 16)
2((5 * -1 + x * -1) + x(5 + x)) = 2 + -1x(2x + 16)
2((-5 + -1x) + x(5 + x)) = 2 + -1x(2x + 16)
2(-5 + -1x + (5 * x + x * x)) = 2 + -1x(2x + 16)
2(-5 + -1x + (5x + x2)) = 2 + -1x(2x + 16)

Combine like terms: -1x + 5x = 4x
2(-5 + 4x + x2) = 2 + -1x(2x + 16)
(-5 * 2 + 4x * 2 + x2 * 2) = 2 + -1x(2x + 16)
(-10 + 8x + 2x2) = 2 + -1x(2x + 16)

Reorder the terms:
-10 + 8x + 2x2 = 2 + -1x(16 + 2x)
-10 + 8x + 2x2 = 2 + (16 * -1x + 2x * -1x)
-10 + 8x + 2x2 = 2 + (-16x + -2x2)

Solving
-10 + 8x + 2x2 = 2 + -16x + -2x2

Solving for variable 'x'.

Reorder the terms:
-10 + -2 + 8x + 16x + 2x2 + 2x2 = 2 + -16x + -2x2 + -2 + 16x + 2x2

Combine like terms: -10 + -2 = -12
-12 + 8x + 16x + 2x2 + 2x2 = 2 + -16x + -2x2 + -2 + 16x + 2x2

Combine like terms: 8x + 16x = 24x
-12 + 24x + 2x2 + 2x2 = 2 + -16x + -2x2 + -2 + 16x + 2x2

Combine like terms: 2x2 + 2x2 = 4x2
-12 + 24x + 4x2 = 2 + -16x + -2x2 + -2 + 16x + 2x2

Reorder the terms:
-12 + 24x + 4x2 = 2 + -2 + -16x + 16x + -2x2 + 2x2

Combine like terms: 2 + -2 = 0
-12 + 24x + 4x2 = 0 + -16x + 16x + -2x2 + 2x2
-12 + 24x + 4x2 = -16x + 16x + -2x2 + 2x2

Combine like terms: -16x + 16x = 0
-12 + 24x + 4x2 = 0 + -2x2 + 2x2
-12 + 24x + 4x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-12 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 6x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + 6x + x2 = 0

Solving
-3 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 6x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6x + x2 = 0 + 3
6x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
6x + x2 = 3

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 = 3 + 9

Reorder the terms:
9 + 6x + x2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6x + x2 = 12

Factor a perfect square on the left side:
(x + 3)(x + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + 3 = 3.464101615

Simplifying
x + 3 = 3.464101615

Reorder the terms:
3 + x = 3.464101615

Solving
3 + x = 3.464101615

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 = 3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.464101615 + -3
x = 3.464101615 + -3

Combine like terms: 3.464101615 + -3 = 0.464101615
x = 0.464101615

Simplifying
x = 0.464101615

Subproblem 2
x + 3 = -3.464101615

Simplifying
x + 3 = -3.464101615

Reorder the terms:
3 + x = -3.464101615

Solving
3 + x = -3.464101615

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 = -3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.464101615 + -3
x = -3.464101615 + -3

Combine like terms: -3.464101615 + -3 = -6.464101615
x = -6.464101615

Simplifying
x = -6.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.464101615, -6.464101615}
Solution
x = {0.464101615, -6.464101615}