5x(2x+5)=180

Solution for 5x(2x+5)=180 equation:

Simplifying
5x(2x + 5) = 180

Reorder the terms:
5x(5 + 2x) = 180
(5 * 5x + 2x * 5x) = 180
(25x + 10x2) = 180

Solving
25x + 10x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 25x + 10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 25x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-36 + 5x + 2x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-36 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-36 + 5x + 2x2 = 0

Solving
-36 + 5x + 2x2 = 0

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

Divide each side by '2'.
-18 + 2.5x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 2.5x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 2.5x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 2.5x + x2 = 0 + 18
2.5x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
2.5x + x2 = 18

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 18 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 18 + 1.5625

Combine like terms: 18 + 1.5625 = 19.5625
1.5625 + 2.5x + x2 = 19.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 19.5625

Calculate the square root of the right side: 4.422951503

Break this problem into two subproblems by setting 
(x + 1.25) equal to 4.422951503 and -4.422951503.

Subproblem 1
x + 1.25 = 4.422951503

Simplifying
x + 1.25 = 4.422951503

Reorder the terms:
1.25 + x = 4.422951503

Solving
1.25 + x = 4.422951503

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 4.422951503 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 4.422951503 + -1.25
x = 4.422951503 + -1.25

Combine like terms: 4.422951503 + -1.25 = 3.172951503
x = 3.172951503

Simplifying
x = 3.172951503

Subproblem 2
x + 1.25 = -4.422951503

Simplifying
x + 1.25 = -4.422951503

Reorder the terms:
1.25 + x = -4.422951503

Solving
1.25 + x = -4.422951503

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -4.422951503 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -4.422951503 + -1.25
x = -4.422951503 + -1.25

Combine like terms: -4.422951503 + -1.25 = -5.672951503
x = -5.672951503

Simplifying
x = -5.672951503

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.172951503, -5.672951503}
Solution
x = {3.172951503, -5.672951503}