12x^2+80x-60=0

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Solution for 12x^2+80x-60=0 equation: 


Simplifying
12x2 + 80x + -60 = 0

Reorder the terms:
-60 + 80x + 12x2 = 0

Solving
-60 + 80x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 20x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15 + 20x + 3x2)' equal to zero and attempt to solve:

Simplifying
-15 + 20x + 3x2 = 0

Solving
-15 + 20x + 3x2 = 0

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

Divide each side by '3'.
-5 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6.666666667x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 6.666666667x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6.666666667x + x2 = 0 + 5
6.666666667x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
6.666666667x + x2 = 5

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 5 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 5 + 11.11111112

Combine like terms: 5 + 11.11111112 = 16.11111112
11.11111112 + 6.666666667x + x2 = 16.11111112

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 16.11111112

Calculate the square root of the right side: 4.013864861

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 4.013864861 and -4.013864861.


Subproblem 1
x + 3.333333334 = 4.013864861

Simplifying
x + 3.333333334 = 4.013864861

Reorder the terms:
3.333333334 + x = 4.013864861

Solving
3.333333334 + x = 4.013864861

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 4.013864861 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 4.013864861 + -3.333333334
x = 4.013864861 + -3.333333334

Combine like terms: 4.013864861 + -3.333333334 = 0.680531527
x = 0.680531527

Simplifying
x = 0.680531527


Subproblem 2
x + 3.333333334 = -4.013864861

Simplifying
x + 3.333333334 = -4.013864861

Reorder the terms:
3.333333334 + x = -4.013864861

Solving
3.333333334 + x = -4.013864861

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -4.013864861 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -4.013864861 + -3.333333334
x = -4.013864861 + -3.333333334

Combine like terms: -4.013864861 + -3.333333334 = -7.347198195
x = -7.347198195

Simplifying
x = -7.347198195


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.680531527, -7.347198195}
Solution
x = {0.680531527, -7.347198195}

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