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Simplifying (6a + -1)(2a + -3) = 0 Reorder the terms: (-1 + 6a)(2a + -3) = 0 Reorder the terms: (-1 + 6a)(-3 + 2a) = 0 Multiply (-1 + 6a) * (-3 + 2a) (-1(-3 + 2a) + 6a * (-3 + 2a)) = 0 ((-3 * -1 + 2a * -1) + 6a * (-3 + 2a)) = 0 ((3 + -2a) + 6a * (-3 + 2a)) = 0 (3 + -2a + (-3 * 6a + 2a * 6a)) = 0 (3 + -2a + (-18a + 12a2)) = 0 Combine like terms: -2a + -18a = -20a (3 + -20a + 12a2) = 0 Solving 3 + -20a + 12a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -6a)(3 + -2a) = 0Subproblem 1
Set the factor '(1 + -6a)' equal to zero and attempt to solve: Simplifying 1 + -6a = 0 Solving 1 + -6a = 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 + -6a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6a = 0 + -1 -6a = 0 + -1 Combine like terms: 0 + -1 = -1 -6a = -1 Divide each side by '-6'. a = 0.1666666667 Simplifying a = 0.1666666667Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {0.1666666667, 1.5}
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