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Simplifying (2a + -4)(7 + -3a) = (5 + 2a)(2a + -4) Reorder the terms: (-4 + 2a)(7 + -3a) = (5 + 2a)(2a + -4) Multiply (-4 + 2a) * (7 + -3a) (-4(7 + -3a) + 2a * (7 + -3a)) = (5 + 2a)(2a + -4) ((7 * -4 + -3a * -4) + 2a * (7 + -3a)) = (5 + 2a)(2a + -4) ((-28 + 12a) + 2a * (7 + -3a)) = (5 + 2a)(2a + -4) (-28 + 12a + (7 * 2a + -3a * 2a)) = (5 + 2a)(2a + -4) (-28 + 12a + (14a + -6a2)) = (5 + 2a)(2a + -4) Combine like terms: 12a + 14a = 26a (-28 + 26a + -6a2) = (5 + 2a)(2a + -4) Reorder the terms: -28 + 26a + -6a2 = (5 + 2a)(-4 + 2a) Multiply (5 + 2a) * (-4 + 2a) -28 + 26a + -6a2 = (5(-4 + 2a) + 2a * (-4 + 2a)) -28 + 26a + -6a2 = ((-4 * 5 + 2a * 5) + 2a * (-4 + 2a)) -28 + 26a + -6a2 = ((-20 + 10a) + 2a * (-4 + 2a)) -28 + 26a + -6a2 = (-20 + 10a + (-4 * 2a + 2a * 2a)) -28 + 26a + -6a2 = (-20 + 10a + (-8a + 4a2)) Combine like terms: 10a + -8a = 2a -28 + 26a + -6a2 = (-20 + 2a + 4a2) Solving -28 + 26a + -6a2 = -20 + 2a + 4a2 Solving for variable 'a'. Reorder the terms: -28 + 20 + 26a + -2a + -6a2 + -4a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2 Combine like terms: -28 + 20 = -8 -8 + 26a + -2a + -6a2 + -4a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2 Combine like terms: 26a + -2a = 24a -8 + 24a + -6a2 + -4a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2 Combine like terms: -6a2 + -4a2 = -10a2 -8 + 24a + -10a2 = -20 + 2a + 4a2 + 20 + -2a + -4a2 Reorder the terms: -8 + 24a + -10a2 = -20 + 20 + 2a + -2a + 4a2 + -4a2 Combine like terms: -20 + 20 = 0 -8 + 24a + -10a2 = 0 + 2a + -2a + 4a2 + -4a2 -8 + 24a + -10a2 = 2a + -2a + 4a2 + -4a2 Combine like terms: 2a + -2a = 0 -8 + 24a + -10a2 = 0 + 4a2 + -4a2 -8 + 24a + -10a2 = 4a2 + -4a2 Combine like terms: 4a2 + -4a2 = 0 -8 + 24a + -10a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 12a + -5a2) = 0 Factor a trinomial. 2((-2 + a)(2 + -5a)) = 0 Ignore the factor 2.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 '(2 + -5a)' equal to zero and attempt to solve: Simplifying 2 + -5a = 0 Solving 2 + -5a = 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 + -5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5a = 0 + -2 -5a = 0 + -2 Combine like terms: 0 + -2 = -2 -5a = -2 Divide each side by '-5'. a = 0.4 Simplifying a = 0.4Solution
a = {2, 0.4}
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