3x*x-30x=360

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Solution for 3x*x-30x=360 equation: 


Simplifying
3x * x + -30x = 360

Multiply x * x
3x2 + -30x = 360

Reorder the terms:
-30x + 3x2 = 360

Solving
-30x + 3x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + -30x + 3x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-120 + -10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-120 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-120 + -10x + x2 = 0

Solving
-120 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -10x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -10x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -10x + x2 = 0 + 120
-10x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-10x + x2 = 120

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 = 120 + 25

Reorder the terms:
25 + -10x + x2 = 120 + 25

Combine like terms: 120 + 25 = 145
25 + -10x + x2 = 145

Factor a perfect square on the left side:
(x + -5)(x + -5) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(x + -5) equal to 12.041594579 and -12.041594579.


Subproblem 1
x + -5 = 12.041594579

Simplifying
x + -5 = 12.041594579

Reorder the terms:
-5 + x = 12.041594579

Solving
-5 + x = 12.041594579

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 = 12.041594579 + 5

Combine like terms: -5 + 5 = 0
0 + x = 12.041594579 + 5
x = 12.041594579 + 5

Combine like terms: 12.041594579 + 5 = 17.041594579
x = 17.041594579

Simplifying
x = 17.041594579


Subproblem 2
x + -5 = -12.041594579

Simplifying
x + -5 = -12.041594579

Reorder the terms:
-5 + x = -12.041594579

Solving
-5 + x = -12.041594579

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 = -12.041594579 + 5

Combine like terms: -5 + 5 = 0
0 + x = -12.041594579 + 5
x = -12.041594579 + 5

Combine like terms: -12.041594579 + 5 = -7.041594579
x = -7.041594579

Simplifying
x = -7.041594579


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.041594579, -7.041594579}
Solution
x = {17.041594579, -7.041594579}

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