(3x+25)(5x-5)=180

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Solution for (3x+25)(5x-5)=180 equation: 


Simplifying
(3x + 25)(5x + -5) = 180

Reorder the terms:
(25 + 3x)(5x + -5) = 180

Reorder the terms:
(25 + 3x)(-5 + 5x) = 180

Multiply (25 + 3x) * (-5 + 5x)
(25(-5 + 5x) + 3x * (-5 + 5x)) = 180
((-5 * 25 + 5x * 25) + 3x * (-5 + 5x)) = 180
((-125 + 125x) + 3x * (-5 + 5x)) = 180
(-125 + 125x + (-5 * 3x + 5x * 3x)) = 180
(-125 + 125x + (-15x + 15x2)) = 180

Combine like terms: 125x + -15x = 110x
(-125 + 110x + 15x2) = 180

Solving
-125 + 110x + 15x2 = 180

Solving for variable 'x'.

Reorder the terms:
-125 + -180 + 110x + 15x2 = 180 + -180

Combine like terms: -125 + -180 = -305
-305 + 110x + 15x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-305 + 110x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-61 + 22x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-61 + 22x + 3x2)' equal to zero and attempt to solve:

Simplifying
-61 + 22x + 3x2 = 0

Solving
-61 + 22x + 3x2 = 0

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

Divide each side by '3'.
-20.33333333 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '20.33333333' to each side of the equation.
-20.33333333 + 7.333333333x + 20.33333333 + x2 = 0 + 20.33333333

Reorder the terms:
-20.33333333 + 20.33333333 + 7.333333333x + x2 = 0 + 20.33333333

Combine like terms: -20.33333333 + 20.33333333 = 0.00000000
0.00000000 + 7.333333333x + x2 = 0 + 20.33333333
7.333333333x + x2 = 0 + 20.33333333

Combine like terms: 0 + 20.33333333 = 20.33333333
7.333333333x + x2 = 20.33333333

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = 20.33333333 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = 20.33333333 + 13.44444445

Combine like terms: 20.33333333 + 13.44444445 = 33.77777778
13.44444445 + 7.333333333x + x2 = 33.77777778

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = 33.77777778

Calculate the square root of the right side: 5.811865258

Break this problem into two subproblems by setting 
(x + 3.666666667) equal to 5.811865258 and -5.811865258.


Subproblem 1
x + 3.666666667 = 5.811865258

Simplifying
x + 3.666666667 = 5.811865258

Reorder the terms:
3.666666667 + x = 5.811865258

Solving
3.666666667 + x = 5.811865258

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = 5.811865258 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = 5.811865258 + -3.666666667
x = 5.811865258 + -3.666666667

Combine like terms: 5.811865258 + -3.666666667 = 2.145198591
x = 2.145198591

Simplifying
x = 2.145198591


Subproblem 2
x + 3.666666667 = -5.811865258

Simplifying
x + 3.666666667 = -5.811865258

Reorder the terms:
3.666666667 + x = -5.811865258

Solving
3.666666667 + x = -5.811865258

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = -5.811865258 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = -5.811865258 + -3.666666667
x = -5.811865258 + -3.666666667

Combine like terms: -5.811865258 + -3.666666667 = -9.478531925
x = -9.478531925

Simplifying
x = -9.478531925


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.145198591, -9.478531925}
Solution
x = {2.145198591, -9.478531925}

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