12x^2-21x-180=0

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Solution for 12x^2-21x-180=0 equation: 


Simplifying
12x2 + -21x + -180 = 0

Reorder the terms:
-180 + -21x + 12x2 = 0

Solving
-180 + -21x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + -7x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + -7x + 4x2)' equal to zero and attempt to solve:

Simplifying
-60 + -7x + 4x2 = 0

Solving
-60 + -7x + 4x2 = 0

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

Divide each side by '4'.
-15 + -1.75x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -1.75x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -1.75x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1.75x + x2 = 0 + 15
-1.75x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-1.75x + x2 = 15

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 15 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 15 + 0.765625

Combine like terms: 15 + 0.765625 = 15.765625
0.765625 + -1.75x + x2 = 15.765625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 15.765625

Calculate the square root of the right side: 3.970595044

Break this problem into two subproblems by setting 
(x + -0.875) equal to 3.970595044 and -3.970595044.


Subproblem 1
x + -0.875 = 3.970595044

Simplifying
x + -0.875 = 3.970595044

Reorder the terms:
-0.875 + x = 3.970595044

Solving
-0.875 + x = 3.970595044

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 3.970595044 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 3.970595044 + 0.875
x = 3.970595044 + 0.875

Combine like terms: 3.970595044 + 0.875 = 4.845595044
x = 4.845595044

Simplifying
x = 4.845595044


Subproblem 2
x + -0.875 = -3.970595044

Simplifying
x + -0.875 = -3.970595044

Reorder the terms:
-0.875 + x = -3.970595044

Solving
-0.875 + x = -3.970595044

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -3.970595044 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -3.970595044 + 0.875
x = -3.970595044 + 0.875

Combine like terms: -3.970595044 + 0.875 = -3.095595044
x = -3.095595044

Simplifying
x = -3.095595044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.845595044, -3.095595044}
Solution
x = {4.845595044, -3.095595044}

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