3g^2-42g+81=0

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Solution for 3g^2-42g+81=0 equation: 


Simplifying
3g2 + -42g + 81 = 0

Reorder the terms:
81 + -42g + 3g2 = 0

Solving
81 + -42g + 3g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + -14g + g2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(27 + -14g + g2)' equal to zero and attempt to solve:

Simplifying
27 + -14g + g2 = 0

Solving
27 + -14g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -14g + -27 + g2 = 0 + -27

Reorder the terms:
27 + -27 + -14g + g2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -14g + g2 = 0 + -27
-14g + g2 = 0 + -27

Combine like terms: 0 + -27 = -27
-14g + g2 = -27

The g term is -14g.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14g + 49 + g2 = -27 + 49

Reorder the terms:
49 + -14g + g2 = -27 + 49

Combine like terms: -27 + 49 = 22
49 + -14g + g2 = 22

Factor a perfect square on the left side:
(g + -7)(g + -7) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(g + -7) equal to 4.69041576 and -4.69041576.


Subproblem 1
g + -7 = 4.69041576

Simplifying
g + -7 = 4.69041576

Reorder the terms:
-7 + g = 4.69041576

Solving
-7 + g = 4.69041576

Solving for variable 'g'.

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

Add '7' to each side of the equation.
-7 + 7 + g = 4.69041576 + 7

Combine like terms: -7 + 7 = 0
0 + g = 4.69041576 + 7
g = 4.69041576 + 7

Combine like terms: 4.69041576 + 7 = 11.69041576
g = 11.69041576

Simplifying
g = 11.69041576


Subproblem 2
g + -7 = -4.69041576

Simplifying
g + -7 = -4.69041576

Reorder the terms:
-7 + g = -4.69041576

Solving
-7 + g = -4.69041576

Solving for variable 'g'.

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

Add '7' to each side of the equation.
-7 + 7 + g = -4.69041576 + 7

Combine like terms: -7 + 7 = 0
0 + g = -4.69041576 + 7
g = -4.69041576 + 7

Combine like terms: -4.69041576 + 7 = 2.30958424
g = 2.30958424

Simplifying
g = 2.30958424


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {11.69041576, 2.30958424}
Solution
g = {11.69041576, 2.30958424}

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