2(x+1)-5(x-3)(2x)=0

Solution for 2(x+1)-5(x-3)(2x)=0 equation:

Simplifying
2(x + 1) + -5(x + -3)(2x) = 0

Reorder the terms:
2(1 + x) + -5(x + -3)(2x) = 0
(1 * 2 + x * 2) + -5(x + -3)(2x) = 0
(2 + 2x) + -5(x + -3)(2x) = 0

Reorder the terms:
2 + 2x + -5(-3 + x)(2x) = 0

Remove parenthesis around (2x)
2 + 2x + -5(-3 + x) * 2x = 0

Reorder the terms for easier multiplication:
2 + 2x + -5 * 2x(-3 + x) = 0

Multiply -5 * 2
2 + 2x + -10x(-3 + x) = 0
2 + 2x + (-3 * -10x + x * -10x) = 0
2 + 2x + (30x + -10x2) = 0

Combine like terms: 2x + 30x = 32x
2 + 32x + -10x2 = 0

Solving
2 + 32x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 16x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 16x + -5x2)' equal to zero and attempt to solve:

Simplifying
1 + 16x + -5x2 = 0

Solving
1 + 16x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.2 + -3.2x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -3.2x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -3.2x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -3.2x + x2 = 0 + 0.2
-3.2x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-3.2x + x2 = 0.2

The x term is -3.2x.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2x + 2.56 + x2 = 0.2 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = 0.2 + 2.56

Combine like terms: 0.2 + 2.56 = 2.76
2.56 + -3.2x + x2 = 2.76

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 2.76

Calculate the square root of the right side: 1.661324773

Break this problem into two subproblems by setting 
(x + -1.6) equal to 1.661324773 and -1.661324773.

Subproblem 1
x + -1.6 = 1.661324773

Simplifying
x + -1.6 = 1.661324773

Reorder the terms:
-1.6 + x = 1.661324773

Solving
-1.6 + x = 1.661324773

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = 1.661324773 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = 1.661324773 + 1.6
x = 1.661324773 + 1.6

Combine like terms: 1.661324773 + 1.6 = 3.261324773
x = 3.261324773

Simplifying
x = 3.261324773

Subproblem 2
x + -1.6 = -1.661324773

Simplifying
x + -1.6 = -1.661324773

Reorder the terms:
-1.6 + x = -1.661324773

Solving
-1.6 + x = -1.661324773

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = -1.661324773 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = -1.661324773 + 1.6
x = -1.661324773 + 1.6

Combine like terms: -1.661324773 + 1.6 = -0.061324773
x = -0.061324773

Simplifying
x = -0.061324773

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.261324773, -0.061324773}
Solution
x = {3.261324773, -0.061324773}