15abc-[4ab^2c+(5a^2bc)-(-4ab^2c-6abc+6a^2bc)]=

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Solution for 15abc-[4ab^2c+(5a^2bc)-(-4ab^2c-6abc+6a^2bc)]= equation: 


Simplifying
15abc + -1[4ab2c + (5a2bc) + -1(-4ab2c + -6abc + 6a2bc)] = 0

Reorder the terms:
15abc + -1[4ab2c + (5a2bc) + -1(-6abc + -4ab2c + 6a2bc)] = 0
15abc + -1[4ab2c + (5a2bc) + (-6abc * -1 + -4ab2c * -1 + 6a2bc * -1)] = 0
15abc + -1[4ab2c + (5a2bc) + (6abc + 4ab2c + -6a2bc)] = 0

Reorder the terms:
15abc + -1[6abc + 4ab2c + 4ab2c + (5a2bc) + -6a2bc] = 0

Combine like terms: 4ab2c + 4ab2c = 8ab2c
15abc + -1[6abc + 8ab2c + (5a2bc) + -6a2bc] = 0

Combine like terms: (5a2bc) + -6a2bc = -1a2bc
15abc + -1[6abc + 8ab2c + -1a2bc] = 0
15abc + [6abc * -1 + 8ab2c * -1 + -1a2bc * -1] = 0
15abc + [-6abc + -8ab2c + 1a2bc] = 0

Combine like terms: 15abc + -6abc = 9abc
9abc + -8ab2c + 1a2bc = 0

Solving
9abc + -8ab2c + 1a2bc = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'abc'.
abc(9 + -8b + a) = 0


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

Simplifying
abc = 0

Solving
abc = 0

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

Simplifying
abc = 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 '(9 + -8b + a)' equal to zero and attempt to solve:

Simplifying
9 + -8b + a = 0

Reorder the terms:
9 + a + -8b = 0

Solving
9 + a + -8b = 0

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

Add '-9' to each side of the equation.
9 + a + -9 + -8b = 0 + -9

Reorder the terms:
9 + -9 + a + -8b = 0 + -9

Combine like terms: 9 + -9 = 0
0 + a + -8b = 0 + -9
a + -8b = 0 + -9

Combine like terms: 0 + -9 = -9
a + -8b = -9

Add '8b' to each side of the equation.
a + -8b + 8b = -9 + 8b

Combine like terms: -8b + 8b = 0
a + 0 = -9 + 8b
a = -9 + 8b

Simplifying
a = -9 + 8b
Solution
a = {-9 + 8b}

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