a(2a+4m)-3a(3a-4m)=0

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Solution for a(2a+4m)-3a(3a-4m)=0 equation: 


Simplifying
a(2a + 4m) + -3a(3a + -4m) = 0
(2a * a + 4m * a) + -3a(3a + -4m) = 0

Reorder the terms:
(4am + 2a2) + -3a(3a + -4m) = 0
(4am + 2a2) + -3a(3a + -4m) = 0
4am + 2a2 + (3a * -3a + -4m * -3a) = 0

Reorder the terms:
4am + 2a2 + (12am + -9a2) = 0
4am + 2a2 + (12am + -9a2) = 0

Reorder the terms:
4am + 12am + 2a2 + -9a2 = 0

Combine like terms: 4am + 12am = 16am
16am + 2a2 + -9a2 = 0

Combine like terms: 2a2 + -9a2 = -7a2
16am + -7a2 = 0

Solving
16am + -7a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(16m + -7a) = 0


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 '(16m + -7a)' equal to zero and attempt to solve:

Simplifying
16m + -7a = 0

Reorder the terms:
-7a + 16m = 0

Solving
-7a + 16m = 0

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

Add '-16m' to each side of the equation.
-7a + 16m + -16m = 0 + -16m

Combine like terms: 16m + -16m = 0
-7a + 0 = 0 + -16m
-7a = 0 + -16m
Remove the zero:
-7a = -16m

Divide each side by '-7'.
a = 2.285714286m

Simplifying
a = 2.285714286m
Solution
a = {0, 2.285714286m}

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