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

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


Simplifying
a(a + -1x) + 3a(x + 2a) + -1a(x + -3a) = 0
(a * a + -1x * a) + 3a(x + 2a) + -1a(x + -3a) = 0

Reorder the terms:
(-1ax + a2) + 3a(x + 2a) + -1a(x + -3a) = 0
(-1ax + a2) + 3a(x + 2a) + -1a(x + -3a) = 0

Reorder the terms:
-1ax + a2 + 3a(2a + x) + -1a(x + -3a) = 0
-1ax + a2 + (2a * 3a + x * 3a) + -1a(x + -3a) = 0

Reorder the terms:
-1ax + a2 + (3ax + 6a2) + -1a(x + -3a) = 0
-1ax + a2 + (3ax + 6a2) + -1a(x + -3a) = 0

Reorder the terms:
-1ax + a2 + 3ax + 6a2 + -1a(-3a + x) = 0
-1ax + a2 + 3ax + 6a2 + (-3a * -1a + x * -1a) = 0

Reorder the terms:
-1ax + a2 + 3ax + 6a2 + (-1ax + 3a2) = 0
-1ax + a2 + 3ax + 6a2 + (-1ax + 3a2) = 0

Reorder the terms:
-1ax + 3ax + -1ax + a2 + 6a2 + 3a2 = 0

Combine like terms: -1ax + 3ax = 2ax
2ax + -1ax + a2 + 6a2 + 3a2 = 0

Combine like terms: 2ax + -1ax = 1ax
1ax + a2 + 6a2 + 3a2 = 0

Combine like terms: a2 + 6a2 = 7a2
1ax + 7a2 + 3a2 = 0

Combine like terms: 7a2 + 3a2 = 10a2
1ax + 10a2 = 0

Solving
1ax + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(x + 10a) = 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 '(x + 10a)' equal to zero and attempt to solve:

Simplifying
x + 10a = 0

Reorder the terms:
10a + x = 0

Solving
10a + x = 0

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

Add '-1x' to each side of the equation.
10a + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
10a + 0 = 0 + -1x
10a = 0 + -1x
Remove the zero:
10a = -1x

Divide each side by '10'.
a = -0.1x

Simplifying
a = -0.1x
Solution
a = {0, -0.1x}

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