12(10-7)+9g=g(2g^2+5)+36

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Solution for 12(10-7)+9g=g(2g^2+5)+36 equation: 


Simplifying
12(10 + -7) + 9g = g(2g2 + 5) + 36

Combine like terms: 10 + -7 = 3
12(3) + 9g = g(2g2 + 5) + 36

Multiply 12 * 3
36 + 9g = g(2g2 + 5) + 36

Reorder the terms:
36 + 9g = g(5 + 2g2) + 36
36 + 9g = (5 * g + 2g2 * g) + 36
36 + 9g = (5g + 2g3) + 36

Reorder the terms:
36 + 9g = 36 + 5g + 2g3

Add '-36' to each side of the equation.
36 + -36 + 9g = 36 + 5g + -36 + 2g3

Combine like terms: 36 + -36 = 0
0 + 9g = 36 + 5g + -36 + 2g3
9g = 36 + 5g + -36 + 2g3

Reorder the terms:
9g = 36 + -36 + 5g + 2g3

Combine like terms: 36 + -36 = 0
9g = 0 + 5g + 2g3
9g = 5g + 2g3

Solving
9g = 5g + 2g3

Solving for variable 'g'.

Combine like terms: 9g + -5g = 4g
4g + -2g3 = 5g + 2g3 + -5g + -2g3

Reorder the terms:
4g + -2g3 = 5g + -5g + 2g3 + -2g3

Combine like terms: 5g + -5g = 0
4g + -2g3 = 0 + 2g3 + -2g3
4g + -2g3 = 2g3 + -2g3

Combine like terms: 2g3 + -2g3 = 0
4g + -2g3 = 0

Factor out the Greatest Common Factor (GCF), '2g'.
2g(2 + -1g2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'g' equal to zero and attempt to solve:

Simplifying
g = 0

Solving
g = 0

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

Simplifying
g = 0

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

Simplifying
2 + -1g2 = 0

Solving
2 + -1g2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1g2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1g2 = 0 + -2
-1g2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1g2 = -2

Divide each side by '-1'.
g2 = 2

Simplifying
g2 = 2

Take the square root of each side:
g = {-1.414213562, 1.414213562}
Solution
g = {0, -1.414213562, 1.414213562}

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