14abc-[3ab^2c+(4a^2bc)-(-3ab^2c-5abc+5a^2bc)]=0

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Solution for 14abc-[3ab^2c+(4a^2bc)-(-3ab^2c-5abc+5a^2bc)]=0 equation:


Simplifying
14abc + -1[3ab2c + (4a2bc) + -1(-3ab2c + -5abc + 5a2bc)] = 0

Reorder the terms:
14abc + -1[3ab2c + (4a2bc) + -1(-5abc + -3ab2c + 5a2bc)] = 0
14abc + -1[3ab2c + (4a2bc) + (-5abc * -1 + -3ab2c * -1 + 5a2bc * -1)] = 0
14abc + -1[3ab2c + (4a2bc) + (5abc + 3ab2c + -5a2bc)] = 0

Reorder the terms:
14abc + -1[5abc + 3ab2c + 3ab2c + (4a2bc) + -5a2bc] = 0

Combine like terms: 3ab2c + 3ab2c = 6ab2c
14abc + -1[5abc + 6ab2c + (4a2bc) + -5a2bc] = 0

Combine like terms: (4a2bc) + -5a2bc = -1a2bc
14abc + -1[5abc + 6ab2c + -1a2bc] = 0
14abc + [5abc * -1 + 6ab2c * -1 + -1a2bc * -1] = 0
14abc + [-5abc + -6ab2c + 1a2bc] = 0

Combine like terms: 14abc + -5abc = 9abc
9abc + -6ab2c + 1a2bc = 0

Solving
9abc + -6ab2c + 1a2bc = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'abc'.
abc(9 + -6b + 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 + -6b + a)' equal to zero and attempt to solve: Simplifying 9 + -6b + a = 0 Reorder the terms: 9 + a + -6b = 0 Solving 9 + a + -6b = 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 + -6b = 0 + -9 Reorder the terms: 9 + -9 + a + -6b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + a + -6b = 0 + -9 a + -6b = 0 + -9 Combine like terms: 0 + -9 = -9 a + -6b = -9 Add '6b' to each side of the equation. a + -6b + 6b = -9 + 6b Combine like terms: -6b + 6b = 0 a + 0 = -9 + 6b a = -9 + 6b Simplifying a = -9 + 6b

Solution

a = {-9 + 6b}

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