x^2+25+3x=(x+3)(2x-1)

Solution for x^2+25+3x=(x+3)(2x-1) equation:

Simplifying
x2 + 25 + 3x = (x + 3)(2x + -1)

Reorder the terms:
25 + 3x + x2 = (x + 3)(2x + -1)

Reorder the terms:
25 + 3x + x2 = (3 + x)(2x + -1)

Reorder the terms:
25 + 3x + x2 = (3 + x)(-1 + 2x)

Multiply (3 + x) * (-1 + 2x)
25 + 3x + x2 = (3(-1 + 2x) + x(-1 + 2x))
25 + 3x + x2 = ((-1 * 3 + 2x * 3) + x(-1 + 2x))
25 + 3x + x2 = ((-3 + 6x) + x(-1 + 2x))
25 + 3x + x2 = (-3 + 6x + (-1 * x + 2x * x))
25 + 3x + x2 = (-3 + 6x + (-1x + 2x2))

Combine like terms: 6x + -1x = 5x
25 + 3x + x2 = (-3 + 5x + 2x2)

Solving
25 + 3x + x2 = -3 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
25 + 3 + 3x + -5x + x2 + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Combine like terms: 25 + 3 = 28
28 + 3x + -5x + x2 + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Combine like terms: 3x + -5x = -2x
28 + -2x + x2 + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Combine like terms: x2 + -2x2 = -1x2
28 + -2x + -1x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Reorder the terms:
28 + -2x + -1x2 = -3 + 3 + 5x + -5x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
28 + -2x + -1x2 = 0 + 5x + -5x + 2x2 + -2x2
28 + -2x + -1x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
28 + -2x + -1x2 = 0 + 2x2 + -2x2
28 + -2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
28 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-28 + 2x + x2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 2x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 2x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 2x + x2 = 0 + 28
2x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
2x + x2 = 28

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 28 + 1

Reorder the terms:
1 + 2x + x2 = 28 + 1

Combine like terms: 28 + 1 = 29
1 + 2x + x2 = 29

Factor a perfect square on the left side:
(x + 1)(x + 1) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + 1) equal to 5.385164807 and -5.385164807.

Subproblem 1
x + 1 = 5.385164807

Simplifying
x + 1 = 5.385164807

Reorder the terms:
1 + x = 5.385164807

Solving
1 + x = 5.385164807

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5.385164807 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.385164807 + -1
x = 5.385164807 + -1

Combine like terms: 5.385164807 + -1 = 4.385164807
x = 4.385164807

Simplifying
x = 4.385164807

Subproblem 2
x + 1 = -5.385164807

Simplifying
x + 1 = -5.385164807

Reorder the terms:
1 + x = -5.385164807

Solving
1 + x = -5.385164807

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5.385164807 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.385164807 + -1
x = -5.385164807 + -1

Combine like terms: -5.385164807 + -1 = -6.385164807
x = -6.385164807

Simplifying
x = -6.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.385164807, -6.385164807}