3g^2-54g+75=0

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Solution for 3g^2-54g+75=0 equation: 


Simplifying
3g2 + -54g + 75 = 0

Reorder the terms:
75 + -54g + 3g2 = 0

Solving
75 + -54g + 3g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + -18g + g2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(25 + -18g + g2)' equal to zero and attempt to solve:

Simplifying
25 + -18g + g2 = 0

Solving
25 + -18g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -18g + -25 + g2 = 0 + -25

Reorder the terms:
25 + -25 + -18g + g2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -18g + g2 = 0 + -25
-18g + g2 = 0 + -25

Combine like terms: 0 + -25 = -25
-18g + g2 = -25

The g term is -18g.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18g + 81 + g2 = -25 + 81

Reorder the terms:
81 + -18g + g2 = -25 + 81

Combine like terms: -25 + 81 = 56
81 + -18g + g2 = 56

Factor a perfect square on the left side:
(g + -9)(g + -9) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(g + -9) equal to 7.483314774 and -7.483314774.


Subproblem 1
g + -9 = 7.483314774

Simplifying
g + -9 = 7.483314774

Reorder the terms:
-9 + g = 7.483314774

Solving
-9 + g = 7.483314774

Solving for variable 'g'.

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

Add '9' to each side of the equation.
-9 + 9 + g = 7.483314774 + 9

Combine like terms: -9 + 9 = 0
0 + g = 7.483314774 + 9
g = 7.483314774 + 9

Combine like terms: 7.483314774 + 9 = 16.483314774
g = 16.483314774

Simplifying
g = 16.483314774


Subproblem 2
g + -9 = -7.483314774

Simplifying
g + -9 = -7.483314774

Reorder the terms:
-9 + g = -7.483314774

Solving
-9 + g = -7.483314774

Solving for variable 'g'.

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

Add '9' to each side of the equation.
-9 + 9 + g = -7.483314774 + 9

Combine like terms: -9 + 9 = 0
0 + g = -7.483314774 + 9
g = -7.483314774 + 9

Combine like terms: -7.483314774 + 9 = 1.516685226
g = 1.516685226

Simplifying
g = 1.516685226


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {16.483314774, 1.516685226}
Solution
g = {16.483314774, 1.516685226}

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