(3x-10)(5x-10)=180

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Solution for (3x-10)(5x-10)=180 equation: 


Simplifying
(3x + -10)(5x + -10) = 180

Reorder the terms:
(-10 + 3x)(5x + -10) = 180

Reorder the terms:
(-10 + 3x)(-10 + 5x) = 180

Multiply (-10 + 3x) * (-10 + 5x)
(-10(-10 + 5x) + 3x * (-10 + 5x)) = 180
((-10 * -10 + 5x * -10) + 3x * (-10 + 5x)) = 180
((100 + -50x) + 3x * (-10 + 5x)) = 180
(100 + -50x + (-10 * 3x + 5x * 3x)) = 180
(100 + -50x + (-30x + 15x2)) = 180

Combine like terms: -50x + -30x = -80x
(100 + -80x + 15x2) = 180

Solving
100 + -80x + 15x2 = 180

Solving for variable 'x'.

Reorder the terms:
100 + -180 + -80x + 15x2 = 180 + -180

Combine like terms: 100 + -180 = -80
-80 + -80x + 15x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-80 + -80x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-16 + -16x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-16 + -16x + 3x2)' equal to zero and attempt to solve:

Simplifying
-16 + -16x + 3x2 = 0

Solving
-16 + -16x + 3x2 = 0

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

Divide each side by '3'.
-5.333333333 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -5.333333333x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -5.333333333x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -5.333333333x + x2 = 0 + 5.333333333
-5.333333333x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-5.333333333x + x2 = 5.333333333

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = 5.333333333 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = 5.333333333 + 7.111111113

Combine like terms: 5.333333333 + 7.111111113 = 12.444444446
7.111111113 + -5.333333333x + x2 = 12.444444446

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 12.444444446

Calculate the square root of the right side: 3.527668415

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 3.527668415 and -3.527668415.


Subproblem 1
x + -2.666666667 = 3.527668415

Simplifying
x + -2.666666667 = 3.527668415

Reorder the terms:
-2.666666667 + x = 3.527668415

Solving
-2.666666667 + x = 3.527668415

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 3.527668415 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 3.527668415 + 2.666666667
x = 3.527668415 + 2.666666667

Combine like terms: 3.527668415 + 2.666666667 = 6.194335082
x = 6.194335082

Simplifying
x = 6.194335082


Subproblem 2
x + -2.666666667 = -3.527668415

Simplifying
x + -2.666666667 = -3.527668415

Reorder the terms:
-2.666666667 + x = -3.527668415

Solving
-2.666666667 + x = -3.527668415

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -3.527668415 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -3.527668415 + 2.666666667
x = -3.527668415 + 2.666666667

Combine like terms: -3.527668415 + 2.666666667 = -0.861001748
x = -0.861001748

Simplifying
x = -0.861001748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.194335082, -0.861001748}
Solution
x = {6.194335082, -0.861001748}

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