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

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


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

Reorder the terms:
x(-2a + x) = 3a(x + -2a)
(-2a * x + x * x) = 3a(x + -2a)
(-2ax + x2) = 3a(x + -2a)

Reorder the terms:
-2ax + x2 = 3a(-2a + x)
-2ax + x2 = (-2a * 3a + x * 3a)

Reorder the terms:
-2ax + x2 = (3ax + -6a2)
-2ax + x2 = (3ax + -6a2)

Solving
-2ax + x2 = 3ax + -6a2

Solving for variable 'a'.

Reorder the terms:
-2ax + -3ax + 6a2 + x2 = 3ax + -6a2 + -3ax + 6a2

Combine like terms: -2ax + -3ax = -5ax
-5ax + 6a2 + x2 = 3ax + -6a2 + -3ax + 6a2

Reorder the terms:
-5ax + 6a2 + x2 = 3ax + -3ax + -6a2 + 6a2

Combine like terms: 3ax + -3ax = 0
-5ax + 6a2 + x2 = 0 + -6a2 + 6a2
-5ax + 6a2 + x2 = -6a2 + 6a2

Combine like terms: -6a2 + 6a2 = 0
-5ax + 6a2 + x2 = 0

Factor a trinomial.
(2a + -1x)(3a + -1x) = 0


Subproblem 1
Set the factor '(2a + -1x)' equal to zero and attempt to solve:

Simplifying
2a + -1x = 0

Solving
2a + -1x = 0

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

Add 'x' to each side of the equation.
2a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
2a + 0 = 0 + x
2a = 0 + x
Remove the zero:
2a = x

Divide each side by '2'.
a = 0.5x

Simplifying
a = 0.5x

Subproblem 2
Set the factor '(3a + -1x)' equal to zero and attempt to solve:

Simplifying
3a + -1x = 0

Solving
3a + -1x = 0

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

Add 'x' to each side of the equation.
3a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
3a + 0 = 0 + x
3a = 0 + x
Remove the zero:
3a = x

Divide each side by '3'.
a = 0.3333333333x

Simplifying
a = 0.3333333333x
Solution
a = {0.5x, 0.3333333333x}

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