12x^2+150x+270=0

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Solution for 12x^2+150x+270=0 equation: 


Simplifying
12x2 + 150x + 270 = 0

Reorder the terms:
270 + 150x + 12x2 = 0

Solving
270 + 150x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(45 + 25x + 2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(45 + 25x + 2x2)' equal to zero and attempt to solve:

Simplifying
45 + 25x + 2x2 = 0

Solving
45 + 25x + 2x2 = 0

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

Divide each side by '2'.
22.5 + 12.5x + x2 = 0

Move the constant term to the right:

Add '-22.5' to each side of the equation.
22.5 + 12.5x + -22.5 + x2 = 0 + -22.5

Reorder the terms:
22.5 + -22.5 + 12.5x + x2 = 0 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + 12.5x + x2 = 0 + -22.5
12.5x + x2 = 0 + -22.5

Combine like terms: 0 + -22.5 = -22.5
12.5x + x2 = -22.5

The x term is 12.5x.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5x + 39.0625 + x2 = -22.5 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = -22.5 + 39.0625

Combine like terms: -22.5 + 39.0625 = 16.5625
39.0625 + 12.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + 6.25) equal to 4.069705149 and -4.069705149.


Subproblem 1
x + 6.25 = 4.069705149

Simplifying
x + 6.25 = 4.069705149

Reorder the terms:
6.25 + x = 4.069705149

Solving
6.25 + x = 4.069705149

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = 4.069705149 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = 4.069705149 + -6.25
x = 4.069705149 + -6.25

Combine like terms: 4.069705149 + -6.25 = -2.180294851
x = -2.180294851

Simplifying
x = -2.180294851


Subproblem 2
x + 6.25 = -4.069705149

Simplifying
x + 6.25 = -4.069705149

Reorder the terms:
6.25 + x = -4.069705149

Solving
6.25 + x = -4.069705149

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = -4.069705149 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = -4.069705149 + -6.25
x = -4.069705149 + -6.25

Combine like terms: -4.069705149 + -6.25 = -10.319705149
x = -10.319705149

Simplifying
x = -10.319705149


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.180294851, -10.319705149}
Solution
x = {-2.180294851, -10.319705149}

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