abs(2a+9)=abs(3a-3)

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Solution for abs(2a+9)=abs(3a-3) equation: 


Simplifying
abs(2a + 9) = abs(3a + -3)

Reorder the terms:
abs(9 + 2a) = abs(3a + -3)
(9 * abs + 2a * abs) = abs(3a + -3)
(9abs + 2a2bs) = abs(3a + -3)

Reorder the terms:
9abs + 2a2bs = abs(-3 + 3a)
9abs + 2a2bs = (-3 * abs + 3a * abs)
9abs + 2a2bs = (-3abs + 3a2bs)

Solving
9abs + 2a2bs = -3abs + 3a2bs

Solving for variable 'a'.

Reorder the terms:
9abs + 3abs + 2a2bs + -3a2bs = -3abs + 3a2bs + 3abs + -3a2bs

Combine like terms: 9abs + 3abs = 12abs
12abs + 2a2bs + -3a2bs = -3abs + 3a2bs + 3abs + -3a2bs

Combine like terms: 2a2bs + -3a2bs = -1a2bs
12abs + -1a2bs = -3abs + 3a2bs + 3abs + -3a2bs

Reorder the terms:
12abs + -1a2bs = -3abs + 3abs + 3a2bs + -3a2bs

Combine like terms: -3abs + 3abs = 0
12abs + -1a2bs = 0 + 3a2bs + -3a2bs
12abs + -1a2bs = 3a2bs + -3a2bs

Combine like terms: 3a2bs + -3a2bs = 0
12abs + -1a2bs = 0

Factor out the Greatest Common Factor (GCF), 'abs'.
abs(12 + -1a) = 0


Subproblem 1
Set the factor 'abs' equal to zero and attempt to solve:

Simplifying
abs = 0

Solving
abs = 0

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

Simplifying
abs = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {12}

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