-36x^2+144x-60=0

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Solution for -36x^2+144x-60=0 equation: 


Simplifying
-36x2 + 144x + -60 = 0

Reorder the terms:
-60 + 144x + -36x2 = 0

Solving
-60 + 144x + -36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-5 + 12x + -3x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-5 + 12x + -3x2)' equal to zero and attempt to solve:

Simplifying
-5 + 12x + -3x2 = 0

Solving
-5 + 12x + -3x2 = 0

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

Divide each side by '-3'.
1.666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -4x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -4x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -4x + x2 = 0 + -1.666666667
-4x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-4x + x2 = -1.666666667

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1.666666667 + 4

Reorder the terms:
4 + -4x + x2 = -1.666666667 + 4

Combine like terms: -1.666666667 + 4 = 2.333333333
4 + -4x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + -2) equal to 1.527525232 and -1.527525232.


Subproblem 1
x + -2 = 1.527525232

Simplifying
x + -2 = 1.527525232

Reorder the terms:
-2 + x = 1.527525232

Solving
-2 + x = 1.527525232

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.527525232 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.527525232 + 2
x = 1.527525232 + 2

Combine like terms: 1.527525232 + 2 = 3.527525232
x = 3.527525232

Simplifying
x = 3.527525232


Subproblem 2
x + -2 = -1.527525232

Simplifying
x + -2 = -1.527525232

Reorder the terms:
-2 + x = -1.527525232

Solving
-2 + x = -1.527525232

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.527525232 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.527525232 + 2
x = -1.527525232 + 2

Combine like terms: -1.527525232 + 2 = 0.472474768
x = 0.472474768

Simplifying
x = 0.472474768


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.527525232, 0.472474768}
Solution
x = {3.527525232, 0.472474768}

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