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Simplifying (4a + -3)(2a + 3a + 5) = 0 Reorder the terms: (-3 + 4a)(2a + 3a + 5) = 0 Reorder the terms: (-3 + 4a)(5 + 2a + 3a) = 0 Combine like terms: 2a + 3a = 5a (-3 + 4a)(5 + 5a) = 0 Multiply (-3 + 4a) * (5 + 5a) (-3(5 + 5a) + 4a * (5 + 5a)) = 0 ((5 * -3 + 5a * -3) + 4a * (5 + 5a)) = 0 ((-15 + -15a) + 4a * (5 + 5a)) = 0 (-15 + -15a + (5 * 4a + 5a * 4a)) = 0 (-15 + -15a + (20a + 20a2)) = 0 Combine like terms: -15a + 20a = 5a (-15 + 5a + 20a2) = 0 Solving -15 + 5a + 20a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + a + 4a2) = 0 Factor a trinomial. 5((-1 + -1a)(3 + -4a)) = 0 Ignore the factor 5.Subproblem 1
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 = -1Subproblem 2
Set the factor '(3 + -4a)' equal to zero and attempt to solve: Simplifying 3 + -4a = 0 Solving 3 + -4a = 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 + -4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a = 0 + -3 -4a = 0 + -3 Combine like terms: 0 + -3 = -3 -4a = -3 Divide each side by '-4'. a = 0.75 Simplifying a = 0.75Solution
a = {-1, 0.75}
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