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Simplifying (5a + -2)(3a + -8) = 0 Reorder the terms: (-2 + 5a)(3a + -8) = 0 Reorder the terms: (-2 + 5a)(-8 + 3a) = 0 Multiply (-2 + 5a) * (-8 + 3a) (-2(-8 + 3a) + 5a * (-8 + 3a)) = 0 ((-8 * -2 + 3a * -2) + 5a * (-8 + 3a)) = 0 ((16 + -6a) + 5a * (-8 + 3a)) = 0 (16 + -6a + (-8 * 5a + 3a * 5a)) = 0 (16 + -6a + (-40a + 15a2)) = 0 Combine like terms: -6a + -40a = -46a (16 + -46a + 15a2) = 0 Solving 16 + -46a + 15a2 = 0 Solving for variable 'a'. Factor a trinomial. (2 + -5a)(8 + -3a) = 0Subproblem 1
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 = 0.4Subproblem 2
Set the factor '(8 + -3a)' equal to zero and attempt to solve: Simplifying 8 + -3a = 0 Solving 8 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3a = 0 + -8 -3a = 0 + -8 Combine like terms: 0 + -8 = -8 -3a = -8 Divide each side by '-3'. a = 2.666666667 Simplifying a = 2.666666667Solution
a = {0.4, 2.666666667}
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