250=(2x+5)(3x-1)

Solution for 250=(2x+5)(3x-1) equation:

Simplifying
250 = (2x + 5)(3x + -1)

Reorder the terms:
250 = (5 + 2x)(3x + -1)

Reorder the terms:
250 = (5 + 2x)(-1 + 3x)

Multiply (5 + 2x) * (-1 + 3x)
250 = (5(-1 + 3x) + 2x * (-1 + 3x))
250 = ((-1 * 5 + 3x * 5) + 2x * (-1 + 3x))
250 = ((-5 + 15x) + 2x * (-1 + 3x))
250 = (-5 + 15x + (-1 * 2x + 3x * 2x))
250 = (-5 + 15x + (-2x + 6x2))

Combine like terms: 15x + -2x = 13x
250 = (-5 + 13x + 6x2)

Solving
250 = -5 + 13x + 6x2

Solving for variable 'x'.

Combine like terms: 250 + 5 = 255
255 + -13x + -6x2 = -5 + 13x + 6x2 + 5 + -13x + -6x2

Reorder the terms:
255 + -13x + -6x2 = -5 + 5 + 13x + -13x + 6x2 + -6x2

Combine like terms: -5 + 5 = 0
255 + -13x + -6x2 = 0 + 13x + -13x + 6x2 + -6x2
255 + -13x + -6x2 = 13x + -13x + 6x2 + -6x2

Combine like terms: 13x + -13x = 0
255 + -13x + -6x2 = 0 + 6x2 + -6x2
255 + -13x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
255 + -13x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-42.5 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '42.5' to each side of the equation.
-42.5 + 2.166666667x + 42.5 + x2 = 0 + 42.5

Reorder the terms:
-42.5 + 42.5 + 2.166666667x + x2 = 0 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + 2.166666667x + x2 = 0 + 42.5
2.166666667x + x2 = 0 + 42.5

Combine like terms: 0 + 42.5 = 42.5
2.166666667x + x2 = 42.5

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = 42.5 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 42.5 + 1.173611113

Combine like terms: 42.5 + 1.173611113 = 43.673611113
1.173611113 + 2.166666667x + x2 = 43.673611113

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 43.673611113

Calculate the square root of the right side: 6.608601298

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 6.608601298 and -6.608601298.

Subproblem 1
x + 1.083333334 = 6.608601298

Simplifying
x + 1.083333334 = 6.608601298

Reorder the terms:
1.083333334 + x = 6.608601298

Solving
1.083333334 + x = 6.608601298

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = 6.608601298 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = 6.608601298 + -1.083333334
x = 6.608601298 + -1.083333334

Combine like terms: 6.608601298 + -1.083333334 = 5.525267964
x = 5.525267964

Simplifying
x = 5.525267964

Subproblem 2
x + 1.083333334 = -6.608601298

Simplifying
x + 1.083333334 = -6.608601298

Reorder the terms:
1.083333334 + x = -6.608601298

Solving
1.083333334 + x = -6.608601298

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = -6.608601298 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = -6.608601298 + -1.083333334
x = -6.608601298 + -1.083333334

Combine like terms: -6.608601298 + -1.083333334 = -7.691934632
x = -7.691934632

Simplifying
x = -7.691934632

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.525267964, -7.691934632}