180=(3x^2)+(12x-30)

Solution for 180=(3x^2)+(12x-30) equation:

Simplifying
180 = (3x2) + (12x + -30)

Reorder the terms:
180 = (3x2) + (-30 + 12x)

Remove parenthesis around (-30 + 12x)
180 = (3x2) + -30 + 12x

Reorder the terms:
180 = -30 + 12x + (3x2)

Solving
180 = -30 + 12x + (3x2)

Solving for variable 'x'.

Combine like terms: 180 + 30 = 210
210 + -12x + (-3x2) = -30 + 12x + (3x2) + 30 + -12x + (-3x2)

Reorder the terms:
210 + -12x + (-3x2) = -30 + 30 + 12x + -12x + (3x2) + (-3x2)

Combine like terms: -30 + 30 = 0
210 + -12x + (-3x2) = 0 + 12x + -12x + (3x2) + (-3x2)
210 + -12x + (-3x2) = 12x + -12x + (3x2) + (-3x2)

Combine like terms: 12x + -12x = 0
210 + -12x + (-3x2) = 0 + (3x2) + (-3x2)
210 + -12x + (-3x2) = (3x2) + (-3x2)

Combine like terms: (3x2) + (-3x2) = 0
210 + -12x + (-3x2) = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(70 + -4x + (-1x2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(70 + -4x + (-1x2))' equal to zero and attempt to solve:

Simplifying
70 + -4x + (-1x2) = 0

Solving
70 + -4x + (-1x2) = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-70 + 4x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 4x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 4x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 4x + x2 = 0 + 70
4x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
4x + x2 = 70

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 70 + 4

Reorder the terms:
4 + 4x + x2 = 70 + 4

Combine like terms: 70 + 4 = 74
4 + 4x + x2 = 74

Factor a perfect square on the left side:
((x) + 2)((x) + 2) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
((x) + 2) equal to 8.602325267 and -8.602325267.

Subproblem 1
(x) + 2 = 8.602325267

Simplifying
(x) + 2 = 8.602325267
x + 2 = 8.602325267

Reorder the terms:
2 + x = 8.602325267

Solving
2 + x = 8.602325267

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 8.602325267 + -2

Combine like terms: 2 + -2 = 0
0 + x = 8.602325267 + -2
x = 8.602325267 + -2

Combine like terms: 8.602325267 + -2 = 6.602325267
x = 6.602325267

Simplifying
x = 6.602325267

Subproblem 2
(x) + 2 = -8.602325267

Simplifying
(x) + 2 = -8.602325267
x + 2 = -8.602325267

Reorder the terms:
2 + x = -8.602325267

Solving
2 + x = -8.602325267

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -8.602325267 + -2

Combine like terms: 2 + -2 = 0
0 + x = -8.602325267 + -2
x = -8.602325267 + -2

Combine like terms: -8.602325267 + -2 = -10.602325267
x = -10.602325267

Simplifying
x = -10.602325267

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.602325267, -10.602325267}
Solution
x = {6.602325267, -10.602325267}