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Simplifying (-5a + 2)(-3a + 4) = 0 Reorder the terms: (2 + -5a)(-3a + 4) = 0 Reorder the terms: (2 + -5a)(4 + -3a) = 0 Multiply (2 + -5a) * (4 + -3a) (2(4 + -3a) + -5a * (4 + -3a)) = 0 ((4 * 2 + -3a * 2) + -5a * (4 + -3a)) = 0 ((8 + -6a) + -5a * (4 + -3a)) = 0 (8 + -6a + (4 * -5a + -3a * -5a)) = 0 (8 + -6a + (-20a + 15a2)) = 0 Combine like terms: -6a + -20a = -26a (8 + -26a + 15a2) = 0 Solving 8 + -26a + 15a2 = 0 Solving for variable 'a'. Factor a trinomial. (2 + -5a)(4 + -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 '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 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 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Solution
a = {0.4, 1.333333333}
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