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Simplifying (4a + -2)(5a + 4) = 0 Reorder the terms: (-2 + 4a)(5a + 4) = 0 Reorder the terms: (-2 + 4a)(4 + 5a) = 0 Multiply (-2 + 4a) * (4 + 5a) (-2(4 + 5a) + 4a * (4 + 5a)) = 0 ((4 * -2 + 5a * -2) + 4a * (4 + 5a)) = 0 ((-8 + -10a) + 4a * (4 + 5a)) = 0 (-8 + -10a + (4 * 4a + 5a * 4a)) = 0 (-8 + -10a + (16a + 20a2)) = 0 Combine like terms: -10a + 16a = 6a (-8 + 6a + 20a2) = 0 Solving -8 + 6a + 20a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 3a + 10a2) = 0 Factor a trinomial. 2((-4 + -5a)(1 + -2a)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.8Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {-0.8, 0.5}
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