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Simplifying (10a + 7)(3a + -9) = 0 Reorder the terms: (7 + 10a)(3a + -9) = 0 Reorder the terms: (7 + 10a)(-9 + 3a) = 0 Multiply (7 + 10a) * (-9 + 3a) (7(-9 + 3a) + 10a * (-9 + 3a)) = 0 ((-9 * 7 + 3a * 7) + 10a * (-9 + 3a)) = 0 ((-63 + 21a) + 10a * (-9 + 3a)) = 0 (-63 + 21a + (-9 * 10a + 3a * 10a)) = 0 (-63 + 21a + (-90a + 30a2)) = 0 Combine like terms: 21a + -90a = -69a (-63 + -69a + 30a2) = 0 Solving -63 + -69a + 30a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + -23a + 10a2) = 0 Factor a trinomial. 3((-7 + -10a)(3 + -1a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -10a)' equal to zero and attempt to solve: Simplifying -7 + -10a = 0 Solving -7 + -10a = 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 + -10a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10a = 0 + 7 -10a = 0 + 7 Combine like terms: 0 + 7 = 7 -10a = 7 Divide each side by '-10'. a = -0.7 Simplifying a = -0.7Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 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 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-0.7, 3}
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