6((x+3)(x+3))+20=12

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Solution for 6((x+3)(x+3))+20=12 equation: 


Simplifying
6((x + 3)(x + 3)) + 20 = 12

Reorder the terms:
6((3 + x)(x + 3)) + 20 = 12

Reorder the terms:
6((3 + x)(3 + x)) + 20 = 12

Multiply (3 + x) * (3 + x)
6((3(3 + x) + x(3 + x))) + 20 = 12
6(((3 * 3 + x * 3) + x(3 + x))) + 20 = 12
6(((9 + 3x) + x(3 + x))) + 20 = 12
6((9 + 3x + (3 * x + x * x))) + 20 = 12
6((9 + 3x + (3x + x2))) + 20 = 12

Combine like terms: 3x + 3x = 6x
6((9 + 6x + x2)) + 20 = 12
(9 * 6 + 6x * 6 + x2 * 6) + 20 = 12
(54 + 36x + 6x2) + 20 = 12

Reorder the terms:
54 + 20 + 36x + 6x2 = 12

Combine like terms: 54 + 20 = 74
74 + 36x + 6x2 = 12

Solving
74 + 36x + 6x2 = 12

Solving for variable 'x'.

Reorder the terms:
74 + -12 + 36x + 6x2 = 12 + -12

Combine like terms: 74 + -12 = 62
62 + 36x + 6x2 = 12 + -12

Combine like terms: 12 + -12 = 0
62 + 36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(31 + 18x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(31 + 18x + 3x2)' equal to zero and attempt to solve:

Simplifying
31 + 18x + 3x2 = 0

Solving
31 + 18x + 3x2 = 0

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

Divide each side by '3'.
10.33333333 + 6x + x2 = 0

Move the constant term to the right:

Add '-10.33333333' to each side of the equation.
10.33333333 + 6x + -10.33333333 + x2 = 0 + -10.33333333

Reorder the terms:
10.33333333 + -10.33333333 + 6x + x2 = 0 + -10.33333333

Combine like terms: 10.33333333 + -10.33333333 = 0.00000000
0.00000000 + 6x + x2 = 0 + -10.33333333
6x + x2 = 0 + -10.33333333

Combine like terms: 0 + -10.33333333 = -10.33333333
6x + x2 = -10.33333333

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -10.33333333 + 9

Reorder the terms:
9 + 6x + x2 = -10.33333333 + 9

Combine like terms: -10.33333333 + 9 = -1.33333333
9 + 6x + x2 = -1.33333333

Factor a perfect square on the left side:
(x + 3)(x + 3) = -1.33333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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