(3x+25)(6x-10)=75

Solution for (3x+25)(6x-10)=75 equation:

Simplifying
(3x + 25)(6x + -10) = 75

Reorder the terms:
(25 + 3x)(6x + -10) = 75

Reorder the terms:
(25 + 3x)(-10 + 6x) = 75

Multiply (25 + 3x) * (-10 + 6x)
(25(-10 + 6x) + 3x * (-10 + 6x)) = 75
((-10 * 25 + 6x * 25) + 3x * (-10 + 6x)) = 75
((-250 + 150x) + 3x * (-10 + 6x)) = 75
(-250 + 150x + (-10 * 3x + 6x * 3x)) = 75
(-250 + 150x + (-30x + 18x2)) = 75

Combine like terms: 150x + -30x = 120x
(-250 + 120x + 18x2) = 75

Solving
-250 + 120x + 18x2 = 75

Solving for variable 'x'.

Reorder the terms:
-250 + -75 + 120x + 18x2 = 75 + -75

Combine like terms: -250 + -75 = -325
-325 + 120x + 18x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-325 + 120x + 18x2 = 0

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

Divide each side by '18'.
-18.05555556 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '18.05555556' to each side of the equation.
-18.05555556 + 6.666666667x + 18.05555556 + x2 = 0 + 18.05555556

Reorder the terms:
-18.05555556 + 18.05555556 + 6.666666667x + x2 = 0 + 18.05555556

Combine like terms: -18.05555556 + 18.05555556 = 0.00000000
0.00000000 + 6.666666667x + x2 = 0 + 18.05555556
6.666666667x + x2 = 0 + 18.05555556

Combine like terms: 0 + 18.05555556 = 18.05555556
6.666666667x + x2 = 18.05555556

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 18.05555556 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 18.05555556 + 11.11111112

Combine like terms: 18.05555556 + 11.11111112 = 29.16666668
11.11111112 + 6.666666667x + x2 = 29.16666668

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 29.16666668

Calculate the square root of the right side: 5.40061725

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 5.40061725 and -5.40061725.

Subproblem 1
x + 3.333333334 = 5.40061725

Simplifying
x + 3.333333334 = 5.40061725

Reorder the terms:
3.333333334 + x = 5.40061725

Solving
3.333333334 + x = 5.40061725

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 5.40061725 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 5.40061725 + -3.333333334
x = 5.40061725 + -3.333333334

Combine like terms: 5.40061725 + -3.333333334 = 2.067283916
x = 2.067283916

Simplifying
x = 2.067283916

Subproblem 2
x + 3.333333334 = -5.40061725

Simplifying
x + 3.333333334 = -5.40061725

Reorder the terms:
3.333333334 + x = -5.40061725

Solving
3.333333334 + x = -5.40061725

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -5.40061725 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -5.40061725 + -3.333333334
x = -5.40061725 + -3.333333334

Combine like terms: -5.40061725 + -3.333333334 = -8.733950584
x = -8.733950584

Simplifying
x = -8.733950584

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.067283916, -8.733950584}