6a^2x-abx-12b^2x=0

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Solution for 6a^2x-abx-12b^2x=0 equation:


Simplifying
6a2x + -1abx + -12b2x = 0

Reorder the terms:
-1abx + 6a2x + -12b2x = 0

Solving
-1abx + 6a2x + -12b2x = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1ab + 6a2 + -12b2) = 0

Factor a trinomial.
x((2a + -3b)(3a + 4b)) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

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 '(2a + -3b)' equal to zero and attempt to solve:

Simplifying
2a + -3b = 0

Solving
2a + -3b = 0

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

Add '3b' to each side of the equation.
2a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
2a + 0 = 0 + 3b
2a = 0 + 3b
Remove the zero:
2a = 3b

Divide each side by '2'.
a = 1.5b

Simplifying
a = 1.5b

Subproblem 3
Set the factor '(3a + 4b)' equal to zero and attempt to solve:

Simplifying
3a + 4b = 0

Solving
3a + 4b = 0

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

Add '-4b' to each side of the equation.
3a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
3a + 0 = 0 + -4b
3a = 0 + -4b
Remove the zero:
3a = -4b

Divide each side by '3'.
a = -1.333333333b

Simplifying
a = -1.333333333b
Solution
a = {1.5b, -1.333333333b}

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