30x^2-12x-1080=0

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Solution for 30x^2-12x-1080=0 equation: 


Simplifying
30x2 + -12x + -1080 = 0

Reorder the terms:
-1080 + -12x + 30x2 = 0

Solving
-1080 + -12x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-180 + -2x + 5x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-180 + -2x + 5x2)' equal to zero and attempt to solve:

Simplifying
-180 + -2x + 5x2 = 0

Solving
-180 + -2x + 5x2 = 0

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

Divide each side by '5'.
-36 + -0.4x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -0.4x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -0.4x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -0.4x + x2 = 0 + 36
-0.4x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-0.4x + x2 = 36

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 36 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 36 + 0.04

Combine like terms: 36 + 0.04 = 36.04
0.04 + -0.4x + x2 = 36.04

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 36.04

Calculate the square root of the right side: 6.003332408

Break this problem into two subproblems by setting 
(x + -0.2) equal to 6.003332408 and -6.003332408.


Subproblem 1
x + -0.2 = 6.003332408

Simplifying
x + -0.2 = 6.003332408

Reorder the terms:
-0.2 + x = 6.003332408

Solving
-0.2 + x = 6.003332408

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = 6.003332408 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = 6.003332408 + 0.2
x = 6.003332408 + 0.2

Combine like terms: 6.003332408 + 0.2 = 6.203332408
x = 6.203332408

Simplifying
x = 6.203332408


Subproblem 2
x + -0.2 = -6.003332408

Simplifying
x + -0.2 = -6.003332408

Reorder the terms:
-0.2 + x = -6.003332408

Solving
-0.2 + x = -6.003332408

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = -6.003332408 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = -6.003332408 + 0.2
x = -6.003332408 + 0.2

Combine like terms: -6.003332408 + 0.2 = -5.803332408
x = -5.803332408

Simplifying
x = -5.803332408


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.203332408, -5.803332408}
Solution
x = {6.203332408, -5.803332408}

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