(6g)(4z)=(3g)(t)

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Solution for (6g)(4z)=(3g)(t) equation: 


Simplifying
(6g)(4z) = (3g)(t)

Remove parenthesis around (6g)
6g(4z) = (3g)(t)

Remove parenthesis around (4z)
6g * 4z = (3g)(t)

Reorder the terms for easier multiplication:
6 * 4g * z = (3g)(t)

Multiply 6 * 4
24g * z = (3g)(t)

Multiply g * z
24gz = (3g)(t)

Remove parenthesis around (3g)
24gz = 3g(t)

Multiply g * t
24gz = 3gt

Solving
24gz = 3gt

Solving for variable 'g'.

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

Add '-3gt' to each side of the equation.
-3gt + 24gz = 3gt + -3gt

Combine like terms: 3gt + -3gt = 0
-3gt + 24gz = 0

Factor out the Greatest Common Factor (GCF), '3g'.
3g(-1t + 8z) = 0

Ignore the factor 3.

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 '(-1t + 8z)' equal to zero and attempt to solve:

Simplifying
-1t + 8z = 0

Solving
-1t + 8z = 0

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

Add 't' to each side of the equation.
-1t + t + 8z = 0 + t

Combine like terms: -1t + t = 0
0 + 8z = 0 + t
8z = 0 + t
Remove the zero:
8z = t

Add '-8z' to each side of the equation.
8z + -8z = t + -8z

Combine like terms: 8z + -8z = 0
0 = t + -8z

Simplifying
0 = t + -8z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
g = {0}

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