((g^2h-3)+(4+3hg^2))-x=(5g^2h-3)

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Solution for ((g^2h-3)+(4+3hg^2))-x=(5g^2h-3) equation:


Simplifying
((g2h + -3) + (4 + 3hg2)) + -1x = (5g2h + -3)

Reorder the terms:
((-3 + g2h) + (4 + 3hg2)) + -1x = (5g2h + -3)

Remove parenthesis around (-3 + g2h)
(-3 + g2h + (4 + 3hg2)) + -1x = (5g2h + -3)

Remove parenthesis around (4 + 3g2h)
(-3 + g2h + 4 + 3g2h) + -1x = (5g2h + -3)

Reorder the terms:
(-3 + 4 + g2h + 3g2h) + -1x = (5g2h + -3)

Combine like terms: -3 + 4 = 1
(1 + g2h + 3g2h) + -1x = (5g2h + -3)

Combine like terms: g2h + 3g2h = 4g2h
(1 + 4g2h) + -1x = (5g2h + -3)

Remove parenthesis around (1 + 4g2h)
1 + 4g2h + -1x = (5g2h + -3)

Reorder the terms:
1 + 4g2h + -1x = (-3 + 5g2h)

Remove parenthesis around (-3 + 5g2h)
1 + 4g2h + -1x = -3 + 5g2h

Solving
1 + 4g2h + -1x = -3 + 5g2h

Solving for variable 'g'.

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

Add '-5g2h' to each side of the equation.
1 + 4g2h + -5g2h + -1x = -3 + 5g2h + -5g2h

Combine like terms: 4g2h + -5g2h = -1g2h
1 + -1g2h + -1x = -3 + 5g2h + -5g2h

Combine like terms: 5g2h + -5g2h = 0
1 + -1g2h + -1x = -3 + 0
1 + -1g2h + -1x = -3

Add '-1' to each side of the equation.
1 + -1g2h + -1 + -1x = -3 + -1

Reorder the terms:
1 + -1 + -1g2h + -1x = -3 + -1

Combine like terms: 1 + -1 = 0
0 + -1g2h + -1x = -3 + -1
-1g2h + -1x = -3 + -1

Combine like terms: -3 + -1 = -4
-1g2h + -1x = -4

Add 'x' to each side of the equation.
-1g2h + -1x + x = -4 + x

Combine like terms: -1x + x = 0
-1g2h + 0 = -4 + x
-1g2h = -4 + x

Divide each side by '-1h'.
g2 = 4h-1 + -1h-1x

Simplifying
g2 = 4h-1 + -1h-1x

Reorder the terms:
g2 + -4h-1 + h-1x = 4h-1 + -4h-1 + -1h-1x + h-1x

Combine like terms: 4h-1 + -4h-1 = 0
g2 + -4h-1 + h-1x = 0 + -1h-1x + h-1x
g2 + -4h-1 + h-1x = -1h-1x + h-1x

Combine like terms: -1h-1x + h-1x = 0
g2 + -4h-1 + h-1x = 0

Factor out the Greatest Common Factor (GCF), 'h-1'.
h-1(g2h + -4 + x) = 0

Subproblem 1

Set the factor 'h-1' equal to zero and attempt to solve: Simplifying h-1 = 0 Solving h-1 = 0 Move all terms containing g to the left, all other terms to the right. Add '-1h-1' to each side of the equation. h-1 + -1h-1 = 0 + -1h-1 Remove the zero: 0 = -1h-1 Simplifying 0 = -1h-1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(g2h + -4 + x)' equal to zero and attempt to solve: Simplifying g2h + -4 + x = 0 Reorder the terms: -4 + g2h + x = 0 Solving -4 + g2h + x = 0 Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + g2h + 4 + x = 0 + 4 Reorder the terms: -4 + 4 + g2h + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + g2h + x = 0 + 4 g2h + x = 0 + 4 Combine like terms: 0 + 4 = 4 g2h + x = 4 Add '-1x' to each side of the equation. g2h + x + -1x = 4 + -1x Combine like terms: x + -1x = 0 g2h + 0 = 4 + -1x g2h = 4 + -1x Divide each side by 'h'. g2 = 4h-1 + -1h-1x Simplifying g2 = 4h-1 + -1h-1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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