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

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

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

Multiply (3 + x) * (5 + -2x)
2 + -1(3(5 + -2x) + x(5 + -2x)) = 0
2 + -1((5 * 3 + -2x * 3) + x(5 + -2x)) = 0
2 + -1((15 + -6x) + x(5 + -2x)) = 0
2 + -1(15 + -6x + (5 * x + -2x * x)) = 0
2 + -1(15 + -6x + (5x + -2x2)) = 0

Combine like terms: -6x + 5x = -1x
2 + -1(15 + -1x + -2x2) = 0
2 + (15 * -1 + -1x * -1 + -2x2 * -1) = 0
2 + (-15 + 1x + 2x2) = 0

Combine like terms: 2 + -15 = -13
-13 + 1x + 2x2 = 0

Solving
-13 + 1x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-6.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 0.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 0.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 0.5x + x2 = 0 + 6.5
0.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
0.5x + x2 = 6.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 6.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 6.5 + 0.0625

Combine like terms: 6.5 + 0.0625 = 6.5625
0.0625 + 0.5x + x2 = 6.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.561737691 and -2.561737691.

Subproblem 1
x + 0.25 = 2.561737691

Simplifying
x + 0.25 = 2.561737691

Reorder the terms:
0.25 + x = 2.561737691

Solving
0.25 + x = 2.561737691

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 2.561737691 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 2.561737691 + -0.25
x = 2.561737691 + -0.25

Combine like terms: 2.561737691 + -0.25 = 2.311737691
x = 2.311737691

Simplifying
x = 2.311737691

Subproblem 2
x + 0.25 = -2.561737691

Simplifying
x + 0.25 = -2.561737691

Reorder the terms:
0.25 + x = -2.561737691

Solving
0.25 + x = -2.561737691

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -2.561737691 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -2.561737691 + -0.25
x = -2.561737691 + -0.25

Combine like terms: -2.561737691 + -0.25 = -2.811737691
x = -2.811737691

Simplifying
x = -2.811737691

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.311737691, -2.811737691}