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Simplifying (1 + -2a)(1 + -3a) = 0 Multiply (1 + -2a) * (1 + -3a) (1(1 + -3a) + -2a * (1 + -3a)) = 0 ((1 * 1 + -3a * 1) + -2a * (1 + -3a)) = 0 ((1 + -3a) + -2a * (1 + -3a)) = 0 (1 + -3a + (1 * -2a + -3a * -2a)) = 0 (1 + -3a + (-2a + 6a2)) = 0 Combine like terms: -3a + -2a = -5a (1 + -5a + 6a2) = 0 Solving 1 + -5a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -3a)(1 + -2a) = 0Subproblem 1
Set the factor '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 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 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 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 = 0.5Solution
a = {0.3333333333, 0.5}
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