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

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


Simplifying
a(3a + -2) + 2a(a + 4) = a(a + 2)

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

Reorder the terms:
-2a + 3a2 + 2a(4 + a) = a(a + 2)
-2a + 3a2 + (4 * 2a + a * 2a) = a(a + 2)
-2a + 3a2 + (8a + 2a2) = a(a + 2)

Reorder the terms:
-2a + 8a + 3a2 + 2a2 = a(a + 2)

Combine like terms: -2a + 8a = 6a
6a + 3a2 + 2a2 = a(a + 2)

Combine like terms: 3a2 + 2a2 = 5a2
6a + 5a2 = a(a + 2)

Reorder the terms:
6a + 5a2 = a(2 + a)
6a + 5a2 = (2 * a + a * a)
6a + 5a2 = (2a + a2)

Solving
6a + 5a2 = 2a + a2

Solving for variable 'a'.

Reorder the terms:
6a + -2a + 5a2 + -1a2 = 2a + a2 + -2a + -1a2

Combine like terms: 6a + -2a = 4a
4a + 5a2 + -1a2 = 2a + a2 + -2a + -1a2

Combine like terms: 5a2 + -1a2 = 4a2
4a + 4a2 = 2a + a2 + -2a + -1a2

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

Combine like terms: 2a + -2a = 0
4a + 4a2 = 0 + a2 + -1a2
4a + 4a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
4a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4a'.
4a(1 + a) = 0

Ignore the factor 4.

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 '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

Simplifying
a = -1
Solution
a = {0, -1}

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