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Simplifying 8a2c + 12ac + 4c = 0 Reorder the terms: 12ac + 8a2c + 4c = 0 Solving 12ac + 8a2c + 4c = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4c'. 4c(3a + 2a2 + 1) = 0 Factor a trinomial. 4c((2a + 1)(a + 1)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing a to the left, all other terms to the right. Add '-1c' to each side of the equation. c + -1c = 0 + -1c Remove the zero: 0 = -1c Simplifying 0 = -1c 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 '(2a + 1)' equal to zero and attempt to solve: Simplifying 2a + 1 = 0 Reorder the terms: 1 + 2a = 0 Solving 1 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2a = 0 + -1 2a = 0 + -1 Combine like terms: 0 + -1 = -1 2a = -1 Divide each side by '2'. a = -0.5 Simplifying a = -0.5Subproblem 3
Set the factor '(a + 1)' equal to zero and attempt to solve: Simplifying a + 1 = 0 Reorder the terms: 1 + a = 0 Solving 1 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Solution
a = {-0.5, -1}
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