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Simplifying 0 = (12b2c + -6a2b3c)(8b2c + -4a2b3c) Reorder the terms: 0 = (-6a2b3c + 12b2c)(8b2c + -4a2b3c) Reorder the terms: 0 = (-6a2b3c + 12b2c)(-4a2b3c + 8b2c) Multiply (-6a2b3c + 12b2c) * (-4a2b3c + 8b2c) 0 = (-6a2b3c * (-4a2b3c + 8b2c) + 12b2c * (-4a2b3c + 8b2c)) 0 = ((-4a2b3c * -6a2b3c + 8b2c * -6a2b3c) + 12b2c * (-4a2b3c + 8b2c)) Reorder the terms: 0 = ((-48a2b5c2 + 24a4b6c2) + 12b2c * (-4a2b3c + 8b2c)) 0 = ((-48a2b5c2 + 24a4b6c2) + 12b2c * (-4a2b3c + 8b2c)) 0 = (-48a2b5c2 + 24a4b6c2 + (-4a2b3c * 12b2c + 8b2c * 12b2c)) 0 = (-48a2b5c2 + 24a4b6c2 + (-48a2b5c2 + 96b4c2)) Reorder the terms: 0 = (-48a2b5c2 + -48a2b5c2 + 24a4b6c2 + 96b4c2) Combine like terms: -48a2b5c2 + -48a2b5c2 = -96a2b5c2 0 = (-96a2b5c2 + 24a4b6c2 + 96b4c2) Solving 0 = -96a2b5c2 + 24a4b6c2 + 96b4c2 Solving for variable 'a'. Remove the zero: 96a2b5c2 + -24a4b6c2 + -96b4c2 = -96a2b5c2 + 24a4b6c2 + 96b4c2 + 96a2b5c2 + -24a4b6c2 + -96b4c2 Reorder the terms: 96a2b5c2 + -24a4b6c2 + -96b4c2 = -96a2b5c2 + 96a2b5c2 + 24a4b6c2 + -24a4b6c2 + 96b4c2 + -96b4c2 Combine like terms: -96a2b5c2 + 96a2b5c2 = 0 96a2b5c2 + -24a4b6c2 + -96b4c2 = 0 + 24a4b6c2 + -24a4b6c2 + 96b4c2 + -96b4c2 96a2b5c2 + -24a4b6c2 + -96b4c2 = 24a4b6c2 + -24a4b6c2 + 96b4c2 + -96b4c2 Combine like terms: 24a4b6c2 + -24a4b6c2 = 0 96a2b5c2 + -24a4b6c2 + -96b4c2 = 0 + 96b4c2 + -96b4c2 96a2b5c2 + -24a4b6c2 + -96b4c2 = 96b4c2 + -96b4c2 Combine like terms: 96b4c2 + -96b4c2 = 0 96a2b5c2 + -24a4b6c2 + -96b4c2 = 0 Factor out the Greatest Common Factor (GCF), '24b4c2'. 24b4c2(4a2b + -1a4b2 + -4) = 0 Factor a trinomial. 24b4c2((-1a2b + 2)(a2b + -2)) = 0 Ignore the factor 24.Subproblem 1
Set the factor 'b4c2' equal to zero and attempt to solve: Simplifying b4c2 = 0 Solving b4c2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b4c2' to each side of the equation. b4c2 + -1b4c2 = 0 + -1b4c2 Remove the zero: 0 = -1b4c2 Simplifying 0 = -1b4c2 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 '(-1a2b + 2)' equal to zero and attempt to solve: Simplifying -1a2b + 2 = 0 Reorder the terms: 2 + -1a2b = 0 Solving 2 + -1a2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a2b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a2b = 0 + -2 -1a2b = 0 + -2 Combine like terms: 0 + -2 = -2 -1a2b = -2 Divide each side by '-1b'. a2 = 2b-1 Simplifying a2 = 2b-1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(a2b + -2)' equal to zero and attempt to solve: Simplifying a2b + -2 = 0 Reorder the terms: -2 + a2b = 0 Solving -2 + a2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a2b = 0 + 2 Combine like terms: -2 + 2 = 0 0 + a2b = 0 + 2 a2b = 0 + 2 Combine like terms: 0 + 2 = 2 a2b = 2 Divide each side by 'b'. a2 = 2b-1 Simplifying a2 = 2b-1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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