6a(3a+2b)=10ab(3a+2b)

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Solution for 6a(3a+2b)=10ab(3a+2b) equation: 


Simplifying
6a(3a + 2b) = 10ab(3a + 2b)
(3a * 6a + 2b * 6a) = 10ab(3a + 2b)

Reorder the terms:
(12ab + 18a2) = 10ab(3a + 2b)
(12ab + 18a2) = 10ab(3a + 2b)
12ab + 18a2 = (3a * 10ab + 2b * 10ab)

Reorder the terms:
12ab + 18a2 = (20ab2 + 30a2b)
12ab + 18a2 = (20ab2 + 30a2b)

Solving
12ab + 18a2 = 20ab2 + 30a2b

Solving for variable 'a'.

Reorder the terms:
12ab + -20ab2 + 18a2 + -30a2b = 20ab2 + 30a2b + -20ab2 + -30a2b

Reorder the terms:
12ab + -20ab2 + 18a2 + -30a2b = 20ab2 + -20ab2 + 30a2b + -30a2b

Combine like terms: 20ab2 + -20ab2 = 0
12ab + -20ab2 + 18a2 + -30a2b = 0 + 30a2b + -30a2b
12ab + -20ab2 + 18a2 + -30a2b = 30a2b + -30a2b

Combine like terms: 30a2b + -30a2b = 0
12ab + -20ab2 + 18a2 + -30a2b = 0

Factor out the Greatest Common Factor (GCF), '2a'.
2a(6b + -10b2 + 9a + -15ab) = 0

Ignore the factor 2.

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(6b + -10b2 + 9a + -15ab)' equal to zero and attempt to solve:

Simplifying
6b + -10b2 + 9a + -15ab = 0

Reorder the terms:
9a + -15ab + 6b + -10b2 = 0

Solving
9a + -15ab + 6b + -10b2 = 0

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

Add '-6b' to each side of the equation.
9a + -15ab + 6b + -6b + -10b2 = 0 + -6b

Combine like terms: 6b + -6b = 0
9a + -15ab + 0 + -10b2 = 0 + -6b
9a + -15ab + -10b2 = 0 + -6b
Remove the zero:
9a + -15ab + -10b2 = -6b

Add '10b2' to each side of the equation.
9a + -15ab + -10b2 + 10b2 = -6b + 10b2

Combine like terms: -10b2 + 10b2 = 0
9a + -15ab + 0 = -6b + 10b2
9a + -15ab = -6b + 10b2

The solution to this equation could not be determined.

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

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