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Simplifying (-2a + 3)(3a + -6) = 0 Reorder the terms: (3 + -2a)(3a + -6) = 0 Reorder the terms: (3 + -2a)(-6 + 3a) = 0 Multiply (3 + -2a) * (-6 + 3a) (3(-6 + 3a) + -2a * (-6 + 3a)) = 0 ((-6 * 3 + 3a * 3) + -2a * (-6 + 3a)) = 0 ((-18 + 9a) + -2a * (-6 + 3a)) = 0 (-18 + 9a + (-6 * -2a + 3a * -2a)) = 0 (-18 + 9a + (12a + -6a2)) = 0 Combine like terms: 9a + 12a = 21a (-18 + 21a + -6a2) = 0 Solving -18 + 21a + -6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 7a + -2a2) = 0 Factor a trinomial. 3((-2 + a)(3 + -2a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + a)' equal to zero and attempt to solve: Simplifying -2 + a = 0 Solving -2 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + a = 0 + 2 a = 0 + 2 Combine like terms: 0 + 2 = 2 a = 2 Simplifying a = 2Subproblem 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 = {2, 1.5}
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