x(-2a)=3a(x-2a)

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Solution for x(-2a)=3a(x-2a) equation: 


Simplifying
x(-2a) = 3a(x + -2a)

Remove parenthesis around (-2a)
x * -2a = 3a(x + -2a)

Reorder the terms for easier multiplication:
-2x * a = 3a(x + -2a)

Multiply x * a
-2ax = 3a(x + -2a)

Reorder the terms:
-2ax = 3a(-2a + x)
-2ax = (-2a * 3a + x * 3a)

Reorder the terms:
-2ax = (3ax + -6a2)
-2ax = (3ax + -6a2)

Solving
-2ax = 3ax + -6a2

Solving for variable 'a'.

Combine like terms: -2ax + -3ax = -5ax
-5ax + 6a2 = 3ax + -6a2 + -3ax + 6a2

Reorder the terms:
-5ax + 6a2 = 3ax + -3ax + -6a2 + 6a2

Combine like terms: 3ax + -3ax = 0
-5ax + 6a2 = 0 + -6a2 + 6a2
-5ax + 6a2 = -6a2 + 6a2

Combine like terms: -6a2 + 6a2 = 0
-5ax + 6a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-5x + 6a) = 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 '(-5x + 6a)' equal to zero and attempt to solve:

Simplifying
-5x + 6a = 0

Reorder the terms:
6a + -5x = 0

Solving
6a + -5x = 0

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

Add '5x' to each side of the equation.
6a + -5x + 5x = 0 + 5x

Combine like terms: -5x + 5x = 0
6a + 0 = 0 + 5x
6a = 0 + 5x
Remove the zero:
6a = 5x

Divide each side by '6'.
a = 0.8333333333x

Simplifying
a = 0.8333333333x
Solution
a = {0, 0.8333333333x}

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