12x^2+24x-12=180

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Solution for 12x^2+24x-12=180 equation: 


Simplifying
12x2 + 24x + -12 = 180

Reorder the terms:
-12 + 24x + 12x2 = 180

Solving
-12 + 24x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
-12 + -180 + 24x + 12x2 = 180 + -180

Combine like terms: -12 + -180 = -192
-192 + 24x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-192 + 24x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-16 + 2x + x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-16 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + 2x + x2 = 0

Solving
-16 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 2x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 2x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 2x + x2 = 0 + 16
2x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
2x + x2 = 16

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 16 + 1

Reorder the terms:
1 + 2x + x2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + 2x + x2 = 17

Factor a perfect square on the left side:
(x + 1)(x + 1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + 1) equal to 4.123105626 and -4.123105626.


Subproblem 1
x + 1 = 4.123105626

Simplifying
x + 1 = 4.123105626

Reorder the terms:
1 + x = 4.123105626

Solving
1 + x = 4.123105626

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.123105626 + -1
x = 4.123105626 + -1

Combine like terms: 4.123105626 + -1 = 3.123105626
x = 3.123105626

Simplifying
x = 3.123105626


Subproblem 2
x + 1 = -4.123105626

Simplifying
x + 1 = -4.123105626

Reorder the terms:
1 + x = -4.123105626

Solving
1 + x = -4.123105626

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.123105626 + -1
x = -4.123105626 + -1

Combine like terms: -4.123105626 + -1 = -5.123105626
x = -5.123105626

Simplifying
x = -5.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.123105626, -5.123105626}
Solution
x = {3.123105626, -5.123105626}

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