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

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


Simplifying
3a(a + 2x) + a2 = a(2 + a)
(a * 3a + 2x * 3a) + a2 = a(2 + a)

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

Combine like terms: 3a2 + a2 = 4a2
6ax + 4a2 = a(2 + a)
6ax + 4a2 = (2 * a + a * a)
6ax + 4a2 = (2a + a2)

Solving
6ax + 4a2 = 2a + a2

Solving for variable 'a'.

Reorder the terms:
-2a + 6ax + 4a2 + -1a2 = 2a + a2 + -2a + -1a2

Combine like terms: 4a2 + -1a2 = 3a2
-2a + 6ax + 3a2 = 2a + a2 + -2a + -1a2

Reorder the terms:
-2a + 6ax + 3a2 = 2a + -2a + a2 + -1a2

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

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(-2 + 6x + 3a) = 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 '(-2 + 6x + 3a)' equal to zero and attempt to solve:

Simplifying
-2 + 6x + 3a = 0

Reorder the terms:
-2 + 3a + 6x = 0

Solving
-2 + 3a + 6x = 0

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

Add '2' to each side of the equation.
-2 + 3a + 2 + 6x = 0 + 2

Reorder the terms:
-2 + 2 + 3a + 6x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3a + 6x = 0 + 2
3a + 6x = 0 + 2

Combine like terms: 0 + 2 = 2
3a + 6x = 2

Add '-6x' to each side of the equation.
3a + 6x + -6x = 2 + -6x

Combine like terms: 6x + -6x = 0
3a + 0 = 2 + -6x
3a = 2 + -6x

Divide each side by '3'.
a = 0.6666666667 + -2x

Simplifying
a = 0.6666666667 + -2x
Solution
a = {0, 0.6666666667 + -2x}

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