6g^2-9g-30=0

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Solution for 6g^2-9g-30=0 equation: 


Simplifying
6g2 + -9g + -30 = 0

Reorder the terms:
-30 + -9g + 6g2 = 0

Solving
-30 + -9g + 6g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -3g + 2g2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-10 + -3g + 2g2)' equal to zero and attempt to solve:

Simplifying
-10 + -3g + 2g2 = 0

Solving
-10 + -3g + 2g2 = 0

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

Divide each side by '2'.
-5 + -1.5g + g2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -1.5g + 5 + g2 = 0 + 5

Reorder the terms:
-5 + 5 + -1.5g + g2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1.5g + g2 = 0 + 5
-1.5g + g2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1.5g + g2 = 5

The g term is -1.5g.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5g + 0.5625 + g2 = 5 + 0.5625

Reorder the terms:
0.5625 + -1.5g + g2 = 5 + 0.5625

Combine like terms: 5 + 0.5625 = 5.5625
0.5625 + -1.5g + g2 = 5.5625

Factor a perfect square on the left side:
(g + -0.75)(g + -0.75) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(g + -0.75) equal to 2.358495283 and -2.358495283.


Subproblem 1
g + -0.75 = 2.358495283

Simplifying
g + -0.75 = 2.358495283

Reorder the terms:
-0.75 + g = 2.358495283

Solving
-0.75 + g = 2.358495283

Solving for variable 'g'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + g = 2.358495283 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + g = 2.358495283 + 0.75
g = 2.358495283 + 0.75

Combine like terms: 2.358495283 + 0.75 = 3.108495283
g = 3.108495283

Simplifying
g = 3.108495283


Subproblem 2
g + -0.75 = -2.358495283

Simplifying
g + -0.75 = -2.358495283

Reorder the terms:
-0.75 + g = -2.358495283

Solving
-0.75 + g = -2.358495283

Solving for variable 'g'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + g = -2.358495283 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + g = -2.358495283 + 0.75
g = -2.358495283 + 0.75

Combine like terms: -2.358495283 + 0.75 = -1.608495283
g = -1.608495283

Simplifying
g = -1.608495283


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {3.108495283, -1.608495283}
Solution
g = {3.108495283, -1.608495283}

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