25x(x+85)=130

Solution for 25x(x+85)=130 equation:

Simplifying
25x(x + 85) = 130

Reorder the terms:
25x(85 + x) = 130
(85 * 25x + x * 25x) = 130
(2125x + 25x2) = 130

Solving
2125x + 25x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + 2125x + 25x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + 2125x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-26 + 425x + 5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-26 + 425x + 5x2)' equal to zero and attempt to solve:

Simplifying
-26 + 425x + 5x2 = 0

Solving
-26 + 425x + 5x2 = 0

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

Divide each side by '5'.
-5.2 + 85x + x2 = 0

Move the constant term to the right:

Add '5.2' to each side of the equation.
-5.2 + 85x + 5.2 + x2 = 0 + 5.2

Reorder the terms:
-5.2 + 5.2 + 85x + x2 = 0 + 5.2

Combine like terms: -5.2 + 5.2 = 0.0
0.0 + 85x + x2 = 0 + 5.2
85x + x2 = 0 + 5.2

Combine like terms: 0 + 5.2 = 5.2
85x + x2 = 5.2

The x term is 85x.  Take half its coefficient (42.5).
Square it (1806.25) and add it to both sides.

Add '1806.25' to each side of the equation.
85x + 1806.25 + x2 = 5.2 + 1806.25

Reorder the terms:
1806.25 + 85x + x2 = 5.2 + 1806.25

Combine like terms: 5.2 + 1806.25 = 1811.45
1806.25 + 85x + x2 = 1811.45

Factor a perfect square on the left side:
(x + 42.5)(x + 42.5) = 1811.45

Calculate the square root of the right side: 42.561132504

Break this problem into two subproblems by setting 
(x + 42.5) equal to 42.561132504 and -42.561132504.

Subproblem 1
x + 42.5 = 42.561132504

Simplifying
x + 42.5 = 42.561132504

Reorder the terms:
42.5 + x = 42.561132504

Solving
42.5 + x = 42.561132504

Solving for variable 'x'.

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

Add '-42.5' to each side of the equation.
42.5 + -42.5 + x = 42.561132504 + -42.5

Combine like terms: 42.5 + -42.5 = 0.0
0.0 + x = 42.561132504 + -42.5
x = 42.561132504 + -42.5

Combine like terms: 42.561132504 + -42.5 = 0.061132504
x = 0.061132504

Simplifying
x = 0.061132504

Subproblem 2
x + 42.5 = -42.561132504

Simplifying
x + 42.5 = -42.561132504

Reorder the terms:
42.5 + x = -42.561132504

Solving
42.5 + x = -42.561132504

Solving for variable 'x'.

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

Add '-42.5' to each side of the equation.
42.5 + -42.5 + x = -42.561132504 + -42.5

Combine like terms: 42.5 + -42.5 = 0.0
0.0 + x = -42.561132504 + -42.5
x = -42.561132504 + -42.5

Combine like terms: -42.561132504 + -42.5 = -85.061132504
x = -85.061132504

Simplifying
x = -85.061132504

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.061132504, -85.061132504}
Solution
x = {0.061132504, -85.061132504}