g^2+2g=2g^2-5g-18

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Solution for g^2+2g=2g^2-5g-18 equation: 


Simplifying
g2 + 2g = 2g2 + -5g + -18

Reorder the terms:
2g + g2 = 2g2 + -5g + -18

Reorder the terms:
2g + g2 = -18 + -5g + 2g2

Solving
2g + g2 = -18 + -5g + 2g2

Solving for variable 'g'.

Reorder the terms:
18 + 2g + 5g + g2 + -2g2 = -18 + -5g + 2g2 + 18 + 5g + -2g2

Combine like terms: 2g + 5g = 7g
18 + 7g + g2 + -2g2 = -18 + -5g + 2g2 + 18 + 5g + -2g2

Combine like terms: g2 + -2g2 = -1g2
18 + 7g + -1g2 = -18 + -5g + 2g2 + 18 + 5g + -2g2

Reorder the terms:
18 + 7g + -1g2 = -18 + 18 + -5g + 5g + 2g2 + -2g2

Combine like terms: -18 + 18 = 0
18 + 7g + -1g2 = 0 + -5g + 5g + 2g2 + -2g2
18 + 7g + -1g2 = -5g + 5g + 2g2 + -2g2

Combine like terms: -5g + 5g = 0
18 + 7g + -1g2 = 0 + 2g2 + -2g2
18 + 7g + -1g2 = 2g2 + -2g2

Combine like terms: 2g2 + -2g2 = 0
18 + 7g + -1g2 = 0

Factor a trinomial.
(9 + -1g)(2 + g) = 0


Subproblem 1
Set the factor '(9 + -1g)' equal to zero and attempt to solve:

Simplifying
9 + -1g = 0

Solving
9 + -1g = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1g = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1g = 0 + -9
-1g = 0 + -9

Combine like terms: 0 + -9 = -9
-1g = -9

Divide each side by '-1'.
g = 9

Simplifying
g = 9

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

Simplifying
2 + g = 0

Solving
2 + g = 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 + g = 0 + -2

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

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

Simplifying
g = -2
Solution
g = {9, -2}

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