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Simplifying (5a + -4)(3a + 2) = 0 Reorder the terms: (-4 + 5a)(3a + 2) = 0 Reorder the terms: (-4 + 5a)(2 + 3a) = 0 Multiply (-4 + 5a) * (2 + 3a) (-4(2 + 3a) + 5a * (2 + 3a)) = 0 ((2 * -4 + 3a * -4) + 5a * (2 + 3a)) = 0 ((-8 + -12a) + 5a * (2 + 3a)) = 0 (-8 + -12a + (2 * 5a + 3a * 5a)) = 0 (-8 + -12a + (10a + 15a2)) = 0 Combine like terms: -12a + 10a = -2a (-8 + -2a + 15a2) = 0 Solving -8 + -2a + 15a2 = 0 Solving for variable 'a'. Factor a trinomial. (-2 + -3a)(4 + -5a) = 0Subproblem 1
Set the factor '(-2 + -3a)' equal to zero and attempt to solve: Simplifying -2 + -3a = 0 Solving -2 + -3a = 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 + -3a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3a = 0 + 2 -3a = 0 + 2 Combine like terms: 0 + 2 = 2 -3a = 2 Divide each side by '-3'. a = -0.6666666667 Simplifying a = -0.6666666667Subproblem 2
Set the factor '(4 + -5a)' equal to zero and attempt to solve: Simplifying 4 + -5a = 0 Solving 4 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5a = 0 + -4 -5a = 0 + -4 Combine like terms: 0 + -4 = -4 -5a = -4 Divide each side by '-5'. a = 0.8 Simplifying a = 0.8Solution
a = {-0.6666666667, 0.8}
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