20x+25x(x+5)=1115

Solution for 20x+25x(x+5)=1115 equation:

Simplifying
20x + 25x(x + 5) = 1115

Reorder the terms:
20x + 25x(5 + x) = 1115
20x + (5 * 25x + x * 25x) = 1115
20x + (125x + 25x2) = 1115

Combine like terms: 20x + 125x = 145x
145x + 25x2 = 1115

Solving
145x + 25x2 = 1115

Solving for variable 'x'.

Reorder the terms:
-1115 + 145x + 25x2 = 1115 + -1115

Combine like terms: 1115 + -1115 = 0
-1115 + 145x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-223 + 29x + 5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-223 + 29x + 5x2)' equal to zero and attempt to solve:

Simplifying
-223 + 29x + 5x2 = 0

Solving
-223 + 29x + 5x2 = 0

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

Divide each side by '5'.
-44.6 + 5.8x + x2 = 0

Move the constant term to the right:

Add '44.6' to each side of the equation.
-44.6 + 5.8x + 44.6 + x2 = 0 + 44.6

Reorder the terms:
-44.6 + 44.6 + 5.8x + x2 = 0 + 44.6

Combine like terms: -44.6 + 44.6 = 0.0
0.0 + 5.8x + x2 = 0 + 44.6
5.8x + x2 = 0 + 44.6

Combine like terms: 0 + 44.6 = 44.6
5.8x + x2 = 44.6

The x term is 5.8x.  Take half its coefficient (2.9).
Square it (8.41) and add it to both sides.

Add '8.41' to each side of the equation.
5.8x + 8.41 + x2 = 44.6 + 8.41

Reorder the terms:
8.41 + 5.8x + x2 = 44.6 + 8.41

Combine like terms: 44.6 + 8.41 = 53.01
8.41 + 5.8x + x2 = 53.01

Factor a perfect square on the left side:
(x + 2.9)(x + 2.9) = 53.01

Calculate the square root of the right side: 7.28079666

Break this problem into two subproblems by setting 
(x + 2.9) equal to 7.28079666 and -7.28079666.

Subproblem 1
x + 2.9 = 7.28079666

Simplifying
x + 2.9 = 7.28079666

Reorder the terms:
2.9 + x = 7.28079666

Solving
2.9 + x = 7.28079666

Solving for variable 'x'.

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

Add '-2.9' to each side of the equation.
2.9 + -2.9 + x = 7.28079666 + -2.9

Combine like terms: 2.9 + -2.9 = 0.0
0.0 + x = 7.28079666 + -2.9
x = 7.28079666 + -2.9

Combine like terms: 7.28079666 + -2.9 = 4.38079666
x = 4.38079666

Simplifying
x = 4.38079666

Subproblem 2
x + 2.9 = -7.28079666

Simplifying
x + 2.9 = -7.28079666

Reorder the terms:
2.9 + x = -7.28079666

Solving
2.9 + x = -7.28079666

Solving for variable 'x'.

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

Add '-2.9' to each side of the equation.
2.9 + -2.9 + x = -7.28079666 + -2.9

Combine like terms: 2.9 + -2.9 = 0.0
0.0 + x = -7.28079666 + -2.9
x = -7.28079666 + -2.9

Combine like terms: -7.28079666 + -2.9 = -10.18079666
x = -10.18079666

Simplifying
x = -10.18079666

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.38079666, -10.18079666}
Solution
x = {4.38079666, -10.18079666}