3A(2A+1)=4A(A-3)

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


Simplifying
3A(2A + 1) = 4A(A + -3)

Reorder the terms:
3A(1 + 2A) = 4A(A + -3)
(1 * 3A + 2A * 3A) = 4A(A + -3)
(3A + 6A2) = 4A(A + -3)

Reorder the terms:
3A + 6A2 = 4A(-3 + A)
3A + 6A2 = (-3 * 4A + A * 4A)
3A + 6A2 = (-12A + 4A2)

Solving
3A + 6A2 = -12A + 4A2

Solving for variable 'A'.

Reorder the terms:
3A + 12A + 6A2 + -4A2 = -12A + 4A2 + 12A + -4A2

Combine like terms: 3A + 12A = 15A
15A + 6A2 + -4A2 = -12A + 4A2 + 12A + -4A2

Combine like terms: 6A2 + -4A2 = 2A2
15A + 2A2 = -12A + 4A2 + 12A + -4A2

Reorder the terms:
15A + 2A2 = -12A + 12A + 4A2 + -4A2

Combine like terms: -12A + 12A = 0
15A + 2A2 = 0 + 4A2 + -4A2
15A + 2A2 = 4A2 + -4A2

Combine like terms: 4A2 + -4A2 = 0
15A + 2A2 = 0

Factor out the Greatest Common Factor (GCF), 'A'.
A(15 + 2A) = 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 '(15 + 2A)' equal to zero and attempt to solve:

Simplifying
15 + 2A = 0

Solving
15 + 2A = 0

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

Add '-15' to each side of the equation.
15 + -15 + 2A = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 2A = 0 + -15
2A = 0 + -15

Combine like terms: 0 + -15 = -15
2A = -15

Divide each side by '2'.
A = -7.5

Simplifying
A = -7.5
Solution
A = {0, -7.5}

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