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Simplifying a(5c + -3) * 4(5c + -3) = 0 Reorder the terms: a(-3 + 5c) * 4(5c + -3) = 0 Reorder the terms: a(-3 + 5c) * 4(-3 + 5c) = 0 Reorder the terms for easier multiplication: 4a(-3 + 5c)(-3 + 5c) = 0 Multiply (-3 + 5c) * (-3 + 5c) 4a(-3(-3 + 5c) + 5c * (-3 + 5c)) = 0 4a((-3 * -3 + 5c * -3) + 5c * (-3 + 5c)) = 0 4a((9 + -15c) + 5c * (-3 + 5c)) = 0 4a(9 + -15c + (-3 * 5c + 5c * 5c)) = 0 4a(9 + -15c + (-15c + 25c2)) = 0 Combine like terms: -15c + -15c = -30c 4a(9 + -30c + 25c2) = 0 (9 * 4a + -30c * 4a + 25c2 * 4a) = 0 (36a + -120ac + 100ac2) = 0 Solving 36a + -120ac + 100ac2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '4a'. 4a(9 + -30c + 25c2) = 0 Factor a trinomial. 4a((3 + -5c)(3 + -5c)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(3 + -5c)' equal to zero and attempt to solve: Simplifying 3 + -5c = 0 Solving 3 + -5c = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5c = 0 + -3 -5c = 0 + -3 Combine like terms: 0 + -3 = -3 -5c = -3 Add '5c' to each side of the equation. -5c + 5c = -3 + 5c Combine like terms: -5c + 5c = 0 0 = -3 + 5c Simplifying 0 = -3 + 5c 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 '(3 + -5c)' equal to zero and attempt to solve: Simplifying 3 + -5c = 0 Solving 3 + -5c = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5c = 0 + -3 -5c = 0 + -3 Combine like terms: 0 + -3 = -3 -5c = -3 Add '5c' to each side of the equation. -5c + 5c = -3 + 5c Combine like terms: -5c + 5c = 0 0 = -3 + 5c Simplifying 0 = -3 + 5c The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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