3x^2-30x-180=0

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Solution for 3x^2-30x-180=0 equation: 


Simplifying
3x2 + -30x + -180 = 0

Reorder the terms:
-180 + -30x + 3x2 = 0

Solving
-180 + -30x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + -10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-60 + -10x + x2 = 0

Solving
-60 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -10x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -10x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -10x + x2 = 0 + 60
-10x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-10x + x2 = 60

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 60 + 25

Reorder the terms:
25 + -10x + x2 = 60 + 25

Combine like terms: 60 + 25 = 85
25 + -10x + x2 = 85

Factor a perfect square on the left side:
(x + -5)(x + -5) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + -5) equal to 9.219544457 and -9.219544457.


Subproblem 1
x + -5 = 9.219544457

Simplifying
x + -5 = 9.219544457

Reorder the terms:
-5 + x = 9.219544457

Solving
-5 + x = 9.219544457

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 9.219544457 + 5

Combine like terms: -5 + 5 = 0
0 + x = 9.219544457 + 5
x = 9.219544457 + 5

Combine like terms: 9.219544457 + 5 = 14.219544457
x = 14.219544457

Simplifying
x = 14.219544457


Subproblem 2
x + -5 = -9.219544457

Simplifying
x + -5 = -9.219544457

Reorder the terms:
-5 + x = -9.219544457

Solving
-5 + x = -9.219544457

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -9.219544457 + 5

Combine like terms: -5 + 5 = 0
0 + x = -9.219544457 + 5
x = -9.219544457 + 5

Combine like terms: -9.219544457 + 5 = -4.219544457
x = -4.219544457

Simplifying
x = -4.219544457


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.219544457, -4.219544457}
Solution
x = {14.219544457, -4.219544457}

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