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Simplifying 4a3 + -4a2 + 3(a2 + -2a) + 3a3 = 0 Reorder the terms: 4a3 + -4a2 + 3(-2a + a2) + 3a3 = 0 4a3 + -4a2 + (-2a * 3 + a2 * 3) + 3a3 = 0 4a3 + -4a2 + (-6a + 3a2) + 3a3 = 0 Reorder the terms: -6a + -4a2 + 3a2 + 4a3 + 3a3 = 0 Combine like terms: -4a2 + 3a2 = -1a2 -6a + -1a2 + 4a3 + 3a3 = 0 Combine like terms: 4a3 + 3a3 = 7a3 -6a + -1a2 + 7a3 = 0 Solving -6a + -1a2 + 7a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-6 + -1a + 7a2) = 0 Factor a trinomial. a((-6 + -7a)(1 + -1a)) = 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 '(-6 + -7a)' equal to zero and attempt to solve: Simplifying -6 + -7a = 0 Solving -6 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -7a = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7a = 0 + 6 -7a = 0 + 6 Combine like terms: 0 + 6 = 6 -7a = 6 Divide each side by '-7'. a = -0.8571428571 Simplifying a = -0.8571428571Subproblem 3
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {0, -0.8571428571, 1}
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