5x(15x+75)=180

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Solution for 5x(15x+75)=180 equation: 


Simplifying
5x(15x + 75) = 180

Reorder the terms:
5x(75 + 15x) = 180
(75 * 5x + 15x * 5x) = 180
(375x + 75x2) = 180

Solving
375x + 75x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 375x + 75x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 375x + 75x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-12 + 25x + 5x2) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(-12 + 25x + 5x2)' equal to zero and attempt to solve:

Simplifying
-12 + 25x + 5x2 = 0

Solving
-12 + 25x + 5x2 = 0

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

Divide each side by '5'.
-2.4 + 5x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 5x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 5x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 5x + x2 = 0 + 2.4
5x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
5x + x2 = 2.4

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2.4 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2.4 + 6.25

Combine like terms: 2.4 + 6.25 = 8.65
6.25 + 5x + x2 = 8.65

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 8.65

Calculate the square root of the right side: 2.941088234

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.941088234 and -2.941088234.


Subproblem 1
x + 2.5 = 2.941088234

Simplifying
x + 2.5 = 2.941088234

Reorder the terms:
2.5 + x = 2.941088234

Solving
2.5 + x = 2.941088234

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.941088234 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.941088234 + -2.5
x = 2.941088234 + -2.5

Combine like terms: 2.941088234 + -2.5 = 0.441088234
x = 0.441088234

Simplifying
x = 0.441088234


Subproblem 2
x + 2.5 = -2.941088234

Simplifying
x + 2.5 = -2.941088234

Reorder the terms:
2.5 + x = -2.941088234

Solving
2.5 + x = -2.941088234

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.941088234 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.941088234 + -2.5
x = -2.941088234 + -2.5

Combine like terms: -2.941088234 + -2.5 = -5.441088234
x = -5.441088234

Simplifying
x = -5.441088234


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.441088234, -5.441088234}
Solution
x = {0.441088234, -5.441088234}

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