(3040g-45200)(-2g^2+59g+30)-(1520g^2-45200g+200)(-4g+59)=0

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Solution for (3040g-45200)(-2g^2+59g+30)-(1520g^2-45200g+200)(-4g+59)=0 equation: 


Simplifying
(3040g + -45200)(-2g2 + 59g + 30) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0

Reorder the terms:
(-45200 + 3040g)(-2g2 + 59g + 30) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0

Reorder the terms:
(-45200 + 3040g)(30 + 59g + -2g2) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0

Multiply (-45200 + 3040g) * (30 + 59g + -2g2)
(-45200(30 + 59g + -2g2) + 3040g * (30 + 59g + -2g2)) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0
((30 * -45200 + 59g * -45200 + -2g2 * -45200) + 3040g * (30 + 59g + -2g2)) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0
((-1356000 + -2666800g + 90400g2) + 3040g * (30 + 59g + -2g2)) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0
(-1356000 + -2666800g + 90400g2 + (30 * 3040g + 59g * 3040g + -2g2 * 3040g)) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0
(-1356000 + -2666800g + 90400g2 + (91200g + 179360g2 + -6080g3)) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0

Reorder the terms:
(-1356000 + -2666800g + 91200g + 90400g2 + 179360g2 + -6080g3) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0

Combine like terms: -2666800g + 91200g = -2575600g
(-1356000 + -2575600g + 90400g2 + 179360g2 + -6080g3) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0

Combine like terms: 90400g2 + 179360g2 = 269760g2
(-1356000 + -2575600g + 269760g2 + -6080g3) + -1(1520g2 + -45200g + 200)(-4g + 59) = 0

Reorder the terms:
-1356000 + -2575600g + 269760g2 + -6080g3 + -1(200 + -45200g + 1520g2)(-4g + 59) = 0

Reorder the terms:
-1356000 + -2575600g + 269760g2 + -6080g3 + -1(200 + -45200g + 1520g2)(59 + -4g) = 0

Multiply (200 + -45200g + 1520g2) * (59 + -4g)
-1356000 + -2575600g + 269760g2 + -6080g3 + -1(200(59 + -4g) + -45200g * (59 + -4g) + 1520g2 * (59 + -4g)) = 0
-1356000 + -2575600g + 269760g2 + -6080g3 + -1((59 * 200 + -4g * 200) + -45200g * (59 + -4g) + 1520g2 * (59 + -4g)) = 0
-1356000 + -2575600g + 269760g2 + -6080g3 + -1((11800 + -800g) + -45200g * (59 + -4g) + 1520g2 * (59 + -4g)) = 0
-1356000 + -2575600g + 269760g2 + -6080g3 + -1(11800 + -800g + (59 * -45200g + -4g * -45200g) + 1520g2 * (59 + -4g)) = 0
-1356000 + -2575600g + 269760g2 + -6080g3 + -1(11800 + -800g + (-2666800g + 180800g2) + 1520g2 * (59 + -4g)) = 0
-1356000 + -2575600g + 269760g2 + -6080g3 + -1(11800 + -800g + -2666800g + 180800g2 + (59 * 1520g2 + -4g * 1520g2)) = 0
-1356000 + -2575600g + 269760g2 + -6080g3 + -1(11800 + -800g + -2666800g + 180800g2 + (89680g2 + -6080g3)) = 0

Combine like terms: -800g + -2666800g = -2667600g
-1356000 + -2575600g + 269760g2 + -6080g3 + -1(11800 + -2667600g + 180800g2 + 89680g2 + -6080g3) = 0

Combine like terms: 180800g2 + 89680g2 = 270480g2
-1356000 + -2575600g + 269760g2 + -6080g3 + -1(11800 + -2667600g + 270480g2 + -6080g3) = 0
-1356000 + -2575600g + 269760g2 + -6080g3 + (11800 * -1 + -2667600g * -1 + 270480g2 * -1 + -6080g3 * -1) = 0
-1356000 + -2575600g + 269760g2 + -6080g3 + (-11800 + 2667600g + -270480g2 + 6080g3) = 0

Reorder the terms:
-1356000 + -11800 + -2575600g + 2667600g + 269760g2 + -270480g2 + -6080g3 + 6080g3 = 0

Combine like terms: -1356000 + -11800 = -1367800
-1367800 + -2575600g + 2667600g + 269760g2 + -270480g2 + -6080g3 + 6080g3 = 0

Combine like terms: -2575600g + 2667600g = 92000g
-1367800 + 92000g + 269760g2 + -270480g2 + -6080g3 + 6080g3 = 0

Combine like terms: 269760g2 + -270480g2 = -720g2
-1367800 + 92000g + -720g2 + -6080g3 + 6080g3 = 0

Combine like terms: -6080g3 + 6080g3 = 0
-1367800 + 92000g + -720g2 + 0 = 0
-1367800 + 92000g + -720g2 = 0

Solving
-1367800 + 92000g + -720g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '40'.
40(-34195 + 2300g + -18g2) = 0

Ignore the factor 40.

Subproblem 1
Set the factor '(-34195 + 2300g + -18g2)' equal to zero and attempt to solve:

Simplifying
-34195 + 2300g + -18g2 = 0

Solving
-34195 + 2300g + -18g2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
1899.722222 + -127.7777778g + g2 = 0

Move the constant term to the right:

Add '-1899.722222' to each side of the equation.
1899.722222 + -127.7777778g + -1899.722222 + g2 = 0 + -1899.722222

Reorder the terms:
1899.722222 + -1899.722222 + -127.7777778g + g2 = 0 + -1899.722222

Combine like terms: 1899.722222 + -1899.722222 = 0.000000
0.000000 + -127.7777778g + g2 = 0 + -1899.722222
-127.7777778g + g2 = 0 + -1899.722222

Combine like terms: 0 + -1899.722222 = -1899.722222
-127.7777778g + g2 = -1899.722222

The g term is -127.7777778g.  Take half its coefficient (-63.8888889).
Square it (4081.790125) and add it to both sides.

Add '4081.790125' to each side of the equation.
-127.7777778g + 4081.790125 + g2 = -1899.722222 + 4081.790125

Reorder the terms:
4081.790125 + -127.7777778g + g2 = -1899.722222 + 4081.790125

Combine like terms: -1899.722222 + 4081.790125 = 2182.067903
4081.790125 + -127.7777778g + g2 = 2182.067903

Factor a perfect square on the left side:
(g + -63.8888889)(g + -63.8888889) = 2182.067903

Calculate the square root of the right side: 46.712609679

Break this problem into two subproblems by setting 
(g + -63.8888889) equal to 46.712609679 and -46.712609679.


Subproblem 1
g + -63.8888889 = 46.712609679

Simplifying
g + -63.8888889 = 46.712609679

Reorder the terms:
-63.8888889 + g = 46.712609679

Solving
-63.8888889 + g = 46.712609679

Solving for variable 'g'.

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

Add '63.8888889' to each side of the equation.
-63.8888889 + 63.8888889 + g = 46.712609679 + 63.8888889

Combine like terms: -63.8888889 + 63.8888889 = 0.0000000
0.0000000 + g = 46.712609679 + 63.8888889
g = 46.712609679 + 63.8888889

Combine like terms: 46.712609679 + 63.8888889 = 110.601498579
g = 110.601498579

Simplifying
g = 110.601498579


Subproblem 2
g + -63.8888889 = -46.712609679

Simplifying
g + -63.8888889 = -46.712609679

Reorder the terms:
-63.8888889 + g = -46.712609679

Solving
-63.8888889 + g = -46.712609679

Solving for variable 'g'.

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

Add '63.8888889' to each side of the equation.
-63.8888889 + 63.8888889 + g = -46.712609679 + 63.8888889

Combine like terms: -63.8888889 + 63.8888889 = 0.0000000
0.0000000 + g = -46.712609679 + 63.8888889
g = -46.712609679 + 63.8888889

Combine like terms: -46.712609679 + 63.8888889 = 17.176279221
g = 17.176279221

Simplifying
g = 17.176279221


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {110.601498579, 17.176279221}
Solution
g = {110.601498579, 17.176279221}

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