2a(3a+4)+6a(2A+1)=

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Solution for 2a(3a+4)+6a(2A+1)= equation: 


Simplifying
2a(3a + 4) + 6a(2A + 1) = 0

Reorder the terms:
2a(4 + 3a) + 6a(2A + 1) = 0
(4 * 2a + 3a * 2a) + 6a(2A + 1) = 0
(8a + 6a2) + 6a(2A + 1) = 0

Reorder the terms:
8a + 6a2 + 6a(1 + 2A) = 0
8a + 6a2 + (1 * 6a + 2A * 6a) = 0
8a + 6a2 + (6a + 12aA) = 0

Reorder the terms:
8a + 6a + 12aA + 6a2 = 0

Combine like terms: 8a + 6a = 14a
14a + 12aA + 6a2 = 0

Solving
14a + 12aA + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(7 + 6A + 3a) = 0

Ignore the factor 2.

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 '(7 + 6A + 3a)' equal to zero and attempt to solve:

Simplifying
7 + 6A + 3a = 0

Solving
7 + 6A + 3a = 0

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

Add '-7' to each side of the equation.
7 + 6A + -7 + 3a = 0 + -7

Reorder the terms:
7 + -7 + 6A + 3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6A + 3a = 0 + -7
6A + 3a = 0 + -7

Combine like terms: 0 + -7 = -7
6A + 3a = -7

Add '-6A' to each side of the equation.
6A + -6A + 3a = -7 + -6A

Combine like terms: 6A + -6A = 0
0 + 3a = -7 + -6A
3a = -7 + -6A

Divide each side by '3'.
a = -2.333333333 + -2A

Simplifying
a = -2.333333333 + -2A
Solution
a = {0, -2.333333333 + -2A}

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