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Simplifying f(-5a) = 3(-5a)(-5a + -4) Remove parenthesis around (-5a) f * -5a = 3(-5a)(-5a + -4) Reorder the terms for easier multiplication: -5f * a = 3(-5a)(-5a + -4) Multiply f * a -5af = 3(-5a)(-5a + -4) Remove parenthesis around (-5a) -5af = 3 * -5a(-5a + -4) Reorder the terms: -5af = 3 * -5a(-4 + -5a) Multiply 3 * -5 -5af = -15a(-4 + -5a) -5af = (-4 * -15a + -5a * -15a) -5af = (60a + 75a2) Solving -5af = 60a + 75a2 Solving for variable 'a'. Reorder the terms: -60a + -5af + -75a2 = 60a + 75a2 + -60a + -75a2 Reorder the terms: -60a + -5af + -75a2 = 60a + -60a + 75a2 + -75a2 Combine like terms: 60a + -60a = 0 -60a + -5af + -75a2 = 0 + 75a2 + -75a2 -60a + -5af + -75a2 = 75a2 + -75a2 Combine like terms: 75a2 + -75a2 = 0 -60a + -5af + -75a2 = 0 Factor out the Greatest Common Factor (GCF), '-5a'. -5a(12 + f + 15a) = 0 Ignore the factor -5.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 '(12 + f + 15a)' equal to zero and attempt to solve: Simplifying 12 + f + 15a = 0 Reorder the terms: 12 + 15a + f = 0 Solving 12 + 15a + f = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 15a + -12 + f = 0 + -12 Reorder the terms: 12 + -12 + 15a + f = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 15a + f = 0 + -12 15a + f = 0 + -12 Combine like terms: 0 + -12 = -12 15a + f = -12 Add '-1f' to each side of the equation. 15a + f + -1f = -12 + -1f Combine like terms: f + -1f = 0 15a + 0 = -12 + -1f 15a = -12 + -1f Divide each side by '15'. a = -0.8 + -0.06666666667f Simplifying a = -0.8 + -0.06666666667fSolution
a = {0, -0.8 + -0.06666666667f}
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