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Simplifying 12a3 + -7a2 + -49a = 0 Reorder the terms: -49a + -7a2 + 12a3 = 0 Solving -49a + -7a2 + 12a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-49 + -7a + 12a2) = 0 Factor a trinomial. a((-7 + -4a)(7 + -3a)) = 0Subproblem 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 '(-7 + -4a)' equal to zero and attempt to solve: Simplifying -7 + -4a = 0 Solving -7 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4a = 0 + 7 -4a = 0 + 7 Combine like terms: 0 + 7 = 7 -4a = 7 Divide each side by '-4'. a = -1.75 Simplifying a = -1.75Subproblem 3
Set the factor '(7 + -3a)' equal to zero and attempt to solve: Simplifying 7 + -3a = 0 Solving 7 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3a = 0 + -7 -3a = 0 + -7 Combine like terms: 0 + -7 = -7 -3a = -7 Divide each side by '-3'. a = 2.333333333 Simplifying a = 2.333333333Solution
a = {0, -1.75, 2.333333333}
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